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Observation of the Standard Model Higgs boson and search for an
additional scalar in the `+`−`+`− final state with the ATLAS detector
by
Xiangyang Ju
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Physics)
at the
University of Wisconsin–Madison
2018
Date of final oral examination: 03.15, 2018
The dissertation is approved by the following members of the Final Oral Committee:
Lisa L Everett, Professor, Physics
Marshall F Onellion, Professor, Physics (material science)
Kimberly J. Palladino, Assistant Professor, Physics
Wesley H Smith, Professor, Physics
Sau Lau Wu, Professor, Physics
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c© Copyright by Xiangyang Ju 2018
All Rights Reserved
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Acknowledgments
First and foremost, I sincerely give my deepest gratitude to my advisor, Prof. Sau
Lan Wu, for her patience, dedication and immense knowledge. It has been a great
honor to join her prestigious group in particle physics. I am deeply grateful for all
her contributions of time, ideas and funding that make my particle physics endeavor
successful.
Besides my advisor, I would like to thank the rest of my thesis committee:
Prof. Lisa Everett, Prof. Marshall Onellion, Prof. Kimberly Palladino and Prof. Wesle
Smith for their insightful comments and encouragement, but also for the hard questions
which incented me to widen my research from various perspectives.
I give my sincere deep thanks to Dr. Kamal Benslama, for educating me with
the fundamental knowledge of particle physics, which, in turn, enabled me to start
physics researches. I enjoyed the days and nights we spent in searching for the first
candidates of W , Z boson and top-pairs using the ATLAS detector.
I was very fortunate to take courses from the outstanding Wisconsin profes-
sors, including Prof. Robert Joynt, Prof. Lisa Everett, Prof. Aki Hashimoto and
Prof. Michael Winokur and many others. They equipped me with the knowledge
needed for future research, for which I really owe them a great thank you.
Distinguished members of the Wisconsin Group have influenced me immensely
in my particle physics endeavor. I want to express my special thanks to Prof. Luis
Roberto Flores Castillo, for supervising me on the search for the Standard Model Higgs
boson in the H → ZZ(∗) → `+`−`+`− final state. I thank Haoshuang Ji and Haichen
Wang for teaching me how to interpret research results using the statistical tools. I
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also thank Laser Kaplan for providing helps in the measurement of the Higgs boson in
the four-lepton channel. At different stages of my Ph.D program, I have been worked
closely with Lashkar Kashif, Fuquan Wang, Andrew Hard, Hongtao Yang and Chen
Zhou on various topics. I value the pleasant time working with them, and I thank
them for all the support and understanding they gave. I thank Neng Xu, Wen Guan,
Shaojun Sun for their timely and continuous support on computing. I also thank other
group members including Lianliang Ma, Swagato Banerjee, Yaquan Fang, Fangzhou
Zhang, Yang Heng, Yao Ming and Alex Wang for their friendship and helps.
I enjoyed my six years in the ATLAS HSG2 (or HZZ) working group, working
with many talented scientists from all overall the world. In the observation of the
Standard Model Higgs analysis, I give my special thanks to Konstantinos Nikolopoulos
and Christos Anastopoulos for their guidance and other helps. The time working
together with them and others including Fabien Tarrade, Eleni Mountricha, Meng
Xiao, Valerio Ippolito and Luis was a precious period in my life, which I cannot
forget. I also thank Marumi Kado and Eilam Gross for their coordination of the
Higgs working group. I thank the group conveners including Stefano Rosati, Rosy
Nikolaidou, Robert Harrington for their coordination of the analyses and support to
me on various aspects.
In the search for additional scalars effort in Run 2, I would like to give my sincere
gratitude to Roberto Di Nardo, Sarah Heim, Arthur Schaffer and Giacomo Artoni for
their insights and guidance throughout all the stages of the analysis. The analysis
would not finish so swiftly and successfully, without the help I received from other
analysis team members. I thank Denys Denysiuk, Graham Cree, Pavel Podberezko,
Syed Haider Abidi, Daniela Paredes Hernandez, and Marc Cano Bret, for their impor-
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tant contributions. I also thank the ATLAS editorial board chaired by Patricia Ward
for ensuring the quality of the publication with admirable amount of effort.
I want to thank Maurice Garcia-Sciveres and Ian Hinchliffe for arranging me
to visit LBNL and work with Maurice on Phase 2 Pixel upgrade. I sincerely thank
the LBNL engineer, Cory Lee, for his support in making different metal parts that I
needed. I am also grateful to the direct helps from Karol Krizka and Timon Heim.
During my short stay in LBNL, I appreciate the friendship of Berkeley colleagues in-
cluding Rebecca Carney, Nikola Whallon, Veronica Wallangen, William Mccormack,
Cesar Gonzalez Renteria, Aleksandra Dimitrievska, Yohei Yamaguchi, Magne Lau-
ritzen, Peilian Liu, Maosen Zhou and many others.
Thank you to my friends from all over the world, particularly Haiyun Teng,
Guoming Liu, Cuihong Huang, Jie Yu, Jin Wang, Liang Sun, Huasheng Shao, Wenli
Wang, Xiaorong Chu, Jie Zhang, Mingming Jiang, Xuan Zhao, Haidong Liang, Chuanzhou
Yi, Weidong Zhou, Jiecheng Ding and Mengyi Xu. Life can be lonely, but I was for-
tunate to have you.
My research cannot go smoothly without the excellent administrative support,
so I would like to thank Rita Knox, Aimee Lefkow, Renne Lefkow and Sylvie Padlewski
for all their kind help.
I want to express my deep gratitude to Bing Zhou, Fabio Cerutti, Arthur Schaf-
fer, Marumi Kado and Konstantinos Nikolopoulos for their valuable time spent in
writing recommendation letters for me when I apply for different post-doctoral posi-
tions. These letters played a crucial role in my applications, for which I really owe
them a great thanks.
Finally, I would like to thank my family for their selfless support throughout my
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pursuing particle physics researches, even though that means less time I can spend
with them. I owe them a debt, which I can never pay back. This thesis is dedicated
to them.
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Contents
LIST OF TABLES viii
LIST OF FIGURES xii
ABSTRACT xxiii
1 Introduction 1
2 The Standard Model and Beyond 5
2.1 Introduction to the Standard Model . . . . . . . . . . . . . . . . . . . . 5
2.2 The Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Higgs boson production and decay mechanisms at the LHC . . . . . . . 8
2.4 Two Higgs Doublet Model . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 The LHC and ATLAS detector 16
3.1 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.3 Muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . 24
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4 Data and Monte Carlo samples 27
4.1 Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 Signal Monte Carlo samples . . . . . . . . . . . . . . . . . . . . 29
4.2.3 Background Monte Carlo samples . . . . . . . . . . . . . . . . . 30
5 Object Reconstruction and Identification 33
5.1 Electron reconstruction and identification . . . . . . . . . . . . . . . . . 34
5.2 Muon reconstruction and identification . . . . . . . . . . . . . . . . . . 37
5.3 Jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6 Analysis Overview 41
6.1 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.2 Inclusive four-lepton event selections . . . . . . . . . . . . . . . . . . . 43
6.3 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.3.2 ``+ µµ background . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.3.3 ``+ ee background . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.4 Statistical methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 The observation of the SM Higgs boson in the `+`−`+`− final state 63
7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.2 Event categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
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7.4 Multivariate techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.5 Signal and background modeling . . . . . . . . . . . . . . . . . . . . . . 71
7.6 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8 Search for additional heavy scalars in the `+`−`+`− final states and
combination with results from `+`−νν final states 83
8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.2 Signal and background modeling . . . . . . . . . . . . . . . . . . . . . . 84
8.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.4 Results and Statistical interpretation . . . . . . . . . . . . . . . . . . . 92
8.4.1 Observed events in signal region . . . . . . . . . . . . . . . . . . 92
8.4.2 p0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.4.3 Upper limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.4.4 2HDM interpretation . . . . . . . . . . . . . . . . . . . . . . . . 99
8.5 Combination of the results from `+`−`+`− and `+`−νν . . . . . . . . . 103
8.5.1 Search for heavy resonances in the `+`−νν final state . . . . . . 103
8.5.2 Correlation schemes . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.5.3 Impact of the uncertainties on signal cross section . . . . . . . . 114
8.5.4 Combination results . . . . . . . . . . . . . . . . . . . . . . . . 116
9 Conclusion 121
REFERENCES 123
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List of Tables
2.1 The Standard Model predictions for the Higgs boson production cross
section together with their theoretical uncertainties. The value of the
Higgs boson mass is assumed to be mH = 125 GeV. The uncertainties in
the cross sections are evaluated as the sum in quadrature of the uncer-
tainties resulting from variations of the QCD scales, parton distribution
functions, and αs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 The branching ratios and the relative uncertainty for a SM Higgs boson
with mH = 125 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.1 Data-driven `` + µµ background estimates for the Run 1 and Run 2
data sets, expressed as yields in the reference control region, for the
combined fits of four control regions. The statistical uncertainties are
also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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6.2 Estimates for the ``+µµ background in the signal region for the full m4`
mass range for the√s = 7 TeV, 8 TeV and 13 TeV data. The Z+jets
and tt background estimates are data-driven and the WZ contribution
is from simulation. The statistical and systematic uncertainties are
presented in a sequential order. The statistical uncertainty for the WZ
contribution is negligible. . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.3 The fit results for the 3` + X control region, the extrapolation factors
and the signal region yields for the reducible `` + ee background. The
sources of background electrons are denoted as light-flavor jets faking
an electron (f), photon conversion (γ) and electrons from heavy-flavor
quark semileptonic decays (q). The second column gives the fit yield of
each component in the 3`+X control region. The corresponding extrap-
olation efficiency and signal region yield are in the next two columns.
The background values represent the sum of the 2µ2e and 4e channels.
The uncertainties are a combination of the statistical and systematic
uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
7.1 The expected number of events in each category (VBF enriched, VH-
hadronic enriched, VH-leptonic enriched, ggF enriched), after all analy-
sis criteria are applied, for each signal production mechanism (ggF/bbH/ttH,
VBF, VH) at mH = 125 GeV, for 4.5 fb−1 at√s = 7 TeV and 20.3 fb−1
at√s = 8 TeV. The requirement m4` > 110 GeV is applied . . . . . . 67
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7.2 Summary of the reducible-background estimates for the data recorded
at√s = 7 TeV and
√s = 8 TeV for the full m4` mass range. The
quoted uncertainties include the combined statistical and systematic
components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3 The expected impact of the systematic uncertainties on the signal yield,
derived from simulation, for mH = 125 GeV, are summarized for each
of the four final states for the combined 2011 and 2012 data sets. The
symbol “-” signifies that the systematic uncertainty does not contribute
to a particular final state. The last three systematic uncertainties apply
equally to all final states. All uncertainties have been symmetrized. . . 79
7.4 The number of events expected and observed for a mH = 125 GeV
hypothesis for the four-lepton final states in a window of 120 < m4` <
130 GeV. The second column shows the number of expected signal
events for the full mass range, without a selection on m4`. The other
columns show for the 120–130 GeV mass range the number of expected
signal events, the number of expected ZZ(∗) and reducible background
events, and the signal-to-background ratio (S/B), together with the
number of observed events for 2011 and 2012 data sets as well as for
the combined sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
8.1 Number of expected and observed events for m4` > 130 GeV, together
with their statistical and systematic uncertainties, for the ggF- and
VBF-enriched categories. . . . . . . . . . . . . . . . . . . . . . . . . . 92
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8.2 Signal acceptance for the `+`−νν analysis, for both the ggF and VBF
production modes and resonance masses of 300 and 600 GeV. The ac-
ceptance is defined as the ratio of the number of reconstructed events
after all selection requirements to the number of simulated events for
each channel/category. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.3 `+`−νν search: Number of expected and observed events together with
their statistical and systematic uncertainties, for the ggF- and VBF-
enriched categories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.4 Impact of the leading systematic uncertainties on the predicted sig-
nal event yield which is set to the expected upper limit, expressed as
a percentage of the cross section for the ggF (left) and VBF (right)
production modes at mH = 300, 600, and 1000 GeV. . . . . . . . . . . 115
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List of Figures
2.1 Elementary particles in the Standard Model, including quarks, leptons,
gauge bosons and the Higgs boson. Their masses, charges and spins are
also presented. Picture is taken from www.wikipedia.com. . . . . . . . 6
2.2 Examples of leading-order Feynman diagrams for Higgs boson produc-
tion via the (a) ggF and (b) VBF production processes. . . . . . . . . 9
2.3 Examples of leading-order Feynman diagrams for Higgs boson produc-
tion via the (a) qq → V H and (b, c) gg → ZH production processes.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Examples of leading-order Feynman diagrams for Higgs production via
the qq/gg → ttH and qq/gg → bbH processes. . . . . . . . . . . . . . . 10
2.5 (a) shows the branching ratio of different Higgs decay modes for different
Higgs boson masses. The theoretical uncertainties are shown as bands.
(b) shows the total width of a SM Higgs boson as a function of the
Higgs mass hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 The luminosity-weighted distribution of the mean number of interac-
tions per bunch crossing for the 2011 and 2012 pp collision data (left),
and 2015 and 2016 pp collision data (right). . . . . . . . . . . . . . . . 19
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3.2 Cut-away view of the ATLAS detector. Its dimensions are 25 m in
height and 44 m in length. The overall weight is approximately 7000 tonnes.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Drawing shows the sensors and structural elements traversed by a charged
track of 10 GeV in the barrel inner detector (the red line). . . . . . . . 23
3.4 Cut-away view of the ATLAS calorimeter system. The electromagnetic
(EM) calorimeter is a sampling liquid-argon (LAr) calorimeter with
lead absorbers. The hadronic calorimeter is a sampling calorimeter with
steel absorbers and active scintillator tiles in the barrel and with copper
absorbers and LAr scintillator in the end-cap. The forward calorimeter
(FCal) consists of copper/LAr and tungsten/LAr. . . . . . . . . . . . . 25
5.1 Combined electron reconstruction and identification efficiencies in Z →
ee events as a function of the transverse energy ET, integrated over
the full pseudo-rapidity range (left), and as a function of pseudorapid-
ity η, integrated over the full ET range (right). The data efficiencies
are obtained from the data-to-MC efficiency ratios measured using J/ψ
and Z tag-and-probe, multiplied by the MC prediction for electrons
from Z → ee decays. The uncertainties are obtained with pseudo-
experiments, treating the statistical uncertainties from the different
(ET, η) bins as uncorrelated. Two sets of uncertainties are shown:
the inner error bars show the statistical uncertainty, the outer error
bars show the combined statistical and systematic uncertainty. . . . . 36
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6.1 The observed m12 distributions (filled circles) and the results of the
maximum likelihood fit are presented for the four control regions using
the Run 1 data sets: (a) inverted criteria on impact parameter signif-
icance, (b) inverted criteria on isolation, (c) eµ leading dilepton, (d)
same-sign subleading dilepton. The fit results are shown for the total
background (black line) as well as the individual components: Z+jets
decomposed into Z + tb, i.e. Z+heavy-flavor jets (blue line) and the
Z+light-flavor jets (green line), tt (dashed red line), and the combined
WZ and ZZ(∗) (dashed gray line), where the WZ and ZZ contributions
are estimated from simulation. . . . . . . . . . . . . . . . . . . . . . . 52
6.2 The observed m12 distributions (filled circles) and the results of the
maximum likelihood fit are presented for the four control regions using
the Run 2 data sets: (a) inverted criteria on impact parameter signif-
icance, (b) inverted criteria on isolation, (c) eµ leading dilepton, (d)
same-sign subleading dilepton. The fit results are shown for the total
background (black line) as well as the individual components: Z+jets
decomposed into Z + tb, i.e. Z+heavy-flavor jets (blue line) and the
Z+light-flavor jets (green line), tt (dashed red line), and the combined
WZ and ZZ(∗) (dashed gray line), where the WZ and ZZ contributions
are estimated from simulation. . . . . . . . . . . . . . . . . . . . . . . 53
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6.3 The results of a simultaneous fit to (a) nB-layerhits , the number of hits in
the innermost pixel layer, and (b) rTRT, the ratio of the number of
high-threshold to low-threshold TRT hits, for the background sources
in the 3` + X control region. The fit is performed separately for the
2µ2e and 4e channels and summed together in the present plots. The
data are represented by the filled circles. The sources of background
electrons are denoted as light-flavor jets faking an electron (f , green
dashed histogram), photon conversion (γ, blue dashed histogram) and
electrons from heavy-flavor quark semileptonic decays (q, red dashed
histogram). The total background is given by the solid blue histogram. 56
6.4 The results of a fit to nInnerPix, the number of IBL hits, or the number
of hits on the next-to-innermost pixel layer when such hits are expected
due to a dead area of the IBL, for background sources in the 3`+X con-
trol region. The fit is performed separately for the 2µ2e and 4e channels
and summed together in the present plots. The data are represented
by the filled circles. The sources of background electrons are denoted
as light-flavor jets faking an electron (f , green dashed histogram) and
photon conversion (γ, yellow filled histogram). The number of elec-
trons from semileptonic decays of heavy-flavor quarks are negligibly
small. The total background is given by the solid red histogram. . . . 57
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7.1 Schematic view of the event categorization. Events are required to
pass the four-lepton selections, and then they are classified into one
of the four categories which are checked sequentially: VBF enriched,
VH-hadronic enriched, VH-leptonic enriched, or ggF enriched. . . . . . 65
7.2 Distributions for signal (blue) and ZZ(∗) background (red) events, show-
ing (a) DZZ(∗) output, (b) p4`T and (c) η4` after the inclusive analysis
selection in the mass range 115 < m4` < 130 GeV used for the training
of the BDTZZ(∗) classifier. (d) output distribution for signal (blue) and
ZZ(∗) background (red) in the mass range of 115 < m4` < 130 GeV. All
histograms are normalized to the same area. . . . . . . . . . . . . . . . 70
7.3 Distributions of kinematic variables for signal (VBF events, green)
and background (ggF events, blue) events used in the training of the
BDTVBF: (a) dijet invariant mass, (b) dijet η separation, (c) leading
jet pT, (d) subleading jet pT, (e) leading jet η, (f) output distributions
of BDTVBF for VBF and ggF events as well as the ZZ(∗) background
(red). All histograms are normalized to the same area. . . . . . . . . . 72
7.4 BDTVH discriminant output for the VH-hadronic enriched category for
signal (VH events, dark blue) and background (ggF events, blue) events. 73
7.5 Probability density for the signal and different backgrounds normalized
to the expected number of events for the 2011 and 2012 data sets,
summing over all the final states: (a) P(m4`, OBDTZZ(∗)|mH) for the
signal assuming mH = 125 GeV, (b) P(m4`, OBDTZZ(∗)
) for the ZZ(∗)
background and (c) P(m4`, OBDTZZ(∗)
) for the reducible background. . 76
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7.6 Invariant mass distribution for a simulated signal sample with mH =
125 GeV, superimposed is the Gaussian fit to the m4` peak after the
correction for final-state radiation and the Z-mass constraint. . . . . . 77
7.7 The distribution of the four-lepton invariant mass, m4`, for the selected
candidates (filled circles) compared to the expected signal and back-
ground contributions (filled histograms) for the combined 2011 and 2012
data sets for the mass range (a) 80–170 GeV, and (b) 80–600 GeV. The
signal expectation shown is for a mass hypothesis of mH = 125 GeV
and normalized to µ = 1.51 (see text). The expected backgrounds
are shown separately for the ZZ(∗) (red histogram), and the reducible
Z+jets and tt backgrounds (violet histogram); the systematic uncer-
tainty associated to the total background contribution is represented
by the hatched areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.8 The observed local p0-value for the combination of the 2011 and 2012
data sets (solid black line) as a function of mH ; the individual results
for√s = 7 TeV and 8 TeV are shown separately as red and blue solid
lines, respectively. The dashed curves show the expected median of the
local p0-value for the signal hypothesis with a signal strength µ = 1,
when evaluated at the corresponding mH . The horizontal dot-dashed
lines indicate the p0-values corresponding to local significances of 1–8 σ. 82
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8.1 (a) Parameterisation of the four-lepton invariant mass (m4`) spectrum
for various resonance mass (mH) hypotheses in the NWA. Markers show
the simulated m4` distribution for three specific values of mH (300,
600, 900 GeV), normalized to unit area, and the dashed lines show
the parameterization used in the 2e2µ channel for these mass points as
well as for intervening ones. (b) RMS of the four-lepton invariant mass
distribution as a function of mH . . . . . . . . . . . . . . . . . . . . . . 85
8.2 Particle-level four-lepton mass m4` model for signal only (red), H–h
interference (green), H–B interference (blue) and the sum of the three
processes (black). Three values of the resonance mass mH (400, 600,
800 GeV) are chosen, as well as three values of the resonance width
ΓH (1%, 5%, 10% of mH). The signal cross section, which determines
the relative contribution of the signal and interference, is taken to be
the cross section of the expected limit for each combination of mH and
ΓH . The full model (black) is finally normalised to unity and the other
contributions are scaled accordingly. . . . . . . . . . . . . . . . . . . . 89
8.3 Distribution of the four-lepton invariant mass m4` in the `+`−`+`− final
state for (a) the ggF-enriched category (b) the VBF-enriched category.
The last bin includes the overflow. The simulated mH = 600 GeV
signal is normalized to a cross section corresponding to five times the
observed limit given in Section 8.5.4. The error bars on the data points
indicate the statistical uncertainty, while the systematic uncertainty in
the prediction is shown by the hatched band. The lower panels show
the ratio of data to the prediction. . . . . . . . . . . . . . . . . . . . . 93
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8.4 Distribution of the four-lepton invariant mass m4` in the `+`−`+`− final
state for (a) the ggF-like 4e category, (b) ggF-like 4µ category and (c)
ggF-like 2µ2e categories category. The error bars on the data points
indicate the statistical uncertainty, while the systematic uncertainty in
the prediction is shown by the hatched band. The lower panels show
the ratio of data to the prediction. . . . . . . . . . . . . . . . . . . . . 94
8.5 Local p0 derived for a narrow resonance and assuming the signal comes
only from the ggF production, as a function of the resonance mass
mH , using the exclusive ggF-like categories, VBF-like categories and the
combined categories. Also shown are local (dot-dashed line) significance
levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.6 Probability distribution function of the maximum local significance in
the full search range 200 < m4` < 1200 GeV, resulting from each of gen-
erated background-only pseudo-experiments. The mean value stands
for the expected local significance resulting from background fluctua-
tion in the full search range. . . . . . . . . . . . . . . . . . . . . . . . 97
8.7 The upper limits at 95% confidence level on then σggF×BR(S → ZZ →
4`) (left) and σV BF ×BR(S → ZZ → 4`) (right) under the NWA. . . . 98
8.8 95% confidence level limits on cross section for ggF production mode
times the branching ratio (σggF × BR(H → ZZ → 4`)) as function of
mH for an additional heavy scalar assuming a width of 1% (a), 5% (b)
and 10% (c) of mH . The green and yellow bands represent the ±1σ and
±2σ uncertainties on the expected limits. . . . . . . . . . . . . . . . . . 100
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8.9 The exclusion contour in the plane of tan β and cos(β − α) for mH =
200 GeV for Type-I and Type-II. The green and yellow bands represent
the ±1σ and ±2σ uncertainties on the expected limits. The hatched
area shows the observed exclusion. . . . . . . . . . . . . . . . . . . . . 101
8.10 The exclusion limits as a function of tan β and mH with cos(β − α) =
−0.1 for Type-I (a) and Type-II (b) 2HDM. The green and yellow
bands represent the ±1σ and ±2σ uncertainties on the expected limits.
The hatched area shows the observed exclusion. . . . . . . . . . . . . . 102
8.11 Missing transverse momentum distribution (a) for events in the 3` con-
trol region as defined in the text and (b) for e±µ∓ lepton pairs after
applying the dilepton invariant mass selection. The backgrounds are
determined following the description in Section 8.5.1 and the last bin
includes the overflow. The error bars on the data points indicate the
statistical uncertainty, while the systematic uncertainty on the predic-
tion is shown by the hatched band. The bottom part of the figures
shows the ratio of data over expectation. . . . . . . . . . . . . . . . . 109
8.12 Transverse invariant mass distribution in the `+`−νν search for (a) the
electron channel and (b) the muon channel, including events from both
the ggF-enriched and the VBF-enriched categories. The backgrounds
are determined following the description in Section 8.5.1 and the last
bin includes the overflow. The error bars on the data points indicate the
statistical uncertainty and markers are drawn at the bin centre. The
systematic uncertainty on the prediction is shown by the hatched band.
The bottom part of the figures shows the ratio of data over expectation. 113
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8.13 Local p0 for `+`−`+`− (blue, dashed line) and `+`−νν (red, dotted line)
final states as well as for their combination (black line) derived for a
narrow resonance and assuming the signal comes only from the ggF
production, as a function of the resonance mass mH between 200 GeV
and 1200 GeV. Also shown are local (dot-dashed line) significance levels. 117
8.14 The upper limits at 95% confidence level on the cross section times
branching ratio for (a) the ggF production mode (σggF × BR(H →
ZZ )) and (b) for the VBF production mode (σVBF ×BR(H → ZZ ))
in the case of NWA. The green and yellow bands represent the ±1σ and
±2σ uncertainties on the expected limits. The dashed coloured lines
indicate the expected limits obtained from the individual searches. . . 118
8.15 The 95% confidence level limits on the cross section for the ggF produc-
tion mode times branching ratio (σggF×BR(H → ZZ )) as function of
mH for an additional heavy scalar assuming a width of (a) 1%, (b) 5%,
and (c) 10% of mH . The green and yellow bands represent the ±1σ and
±2σ uncertainties on the expected limits. The dashed coloured lines
indicate the expected limits obtained from the individual searches. . . 120
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Observation of the Standard Model Higgs boson and search for an
additional scalar in the `+`−`+`− final state with the ATLAS detector
Xiangyang Ju
Under the supervision of Professor Sau Lan Wu
At the University of Wisconsin–Madison
Abstract
This thesis presents the observation of a Standard Model Higgs boson (h) and
a search for an additional scalar (H) in the h/H → ZZ(∗) → `+`−`+`− channel (four-
lepton channel), where ` stands for either an electron or a muon. The observation
of a Standard Model Higgs boson in the four-lepton channel uses the proton–proton
collision data collected with the ATLAS detector during 2011 and 2012 at center-
of-mass energies of 7 and 8 TeV. An excess with a local significance of 8.1 standard
deviation is observed in the four-lepton invariant mass spectrum around 125 GeV.
The mass of the excess measured in `+`−`+`− channel is 125.51 ± 0.52 GeV. Further
measurements on the production cross section times branching ratio of the excess agree
well with the Standard Model predictions within the experimental uncertainties.
The search for an additional scalar uses an integrated luminosity of 36.1 fb−1
proton–proton collision data at a center-of-mass energy of 13 TeV collected with the
ATLAS detector during 2015 and 2016. The results of the search are interpreted as
upper limits on the production cross section of a spin-0 resonance. The mass range
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of the hypothesized additional scalar considered is between 200 GeVand 1.2 TeV. The
upper limits for the spin-0 resonance are translated to exclusion contours in the content
of Type-I and Type-II two-Higgs-doublet models. This analysis is combined with the
same search in the H → ZZ → `+`−νν channel to enhance the search sensitivities in
the high mass region.
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Chapter 1
Introduction
The Higgs mechanism [1–5] plays a central role in providing mass to the W and Z
vector bosons without violating local gauge invariance. In the Standard Model (SM)
of particle physics [6–8], the Higgs mechanism implies a neutral and colorless scalar
particle, the Higgs boson. The search for the Higgs boson is the highlight of the Large
Hadron Collider (LHC) physics program [9].
Indirect experimental limits on the Higgs boson mass of mH < 158 GeV at 95%
confidence level (CL) are obtained from precision measurements of the electroweak
parameters that depend logarithmically on the Higgs boson mass through radiative
corrections [10]. Direct searches at the Large Electron-Positron Collider (LEP) at
CERN placed a lower bound of 114.4 GeV on the Higgs boson mass at 95% CL,
using a total of about 2.46 pb−1 of e+e− collision data at center-of-mass (√s) energies
between 189 and 209 GeV [11]. The searches for the SM Higgs boson in A Toroidal
LHC Apparatus (ATLAS) and Compact Muon Solenoid (CMS) cover all major Higgs
decay channels, including H → bb, H → W+W−, H → γγ, H → ZZ and H → ττ .
This thesis presents the observation of a SM Higgs boson in the H→ ZZ(∗) → `+`−`+`−
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2
decay channel (four-lepton channel) in pp collisions at center-of-mass energies of 7 and
8 TeV with the ATLAS detector at the LHC.
On July 4th 2012, the ATLAS and CMS collaboration independently announced
the observation of a new particle using pp collision data at center-of-mass energies of 7
and 8 TeV produced by the LHC [12,13]. Three years later, by combining the ATLAS
and CMS results, the mass of the discovered particle was precisely measured [14]:
125.09 ± 0.21(stat) ± 0.11(sys) GeV
Once its mass was determined, other properties of the Higgs boson could be theo-
retically calculated and experimentally checked. There has been great progress in
understanding the main properties of the observed particle: (1) its spin and CP were
tested against some other alternative assumptions, which have been excluded at more
than 99.9% confidence level using the ATLAS and CMS detectors [15–17]; (2) its CP
invariance in the vector boson fusion production were tested in di-tau decay channel
and found to be consistent with the SM expectation [18]; (3) its production and decay
rates were measured using the combined ATLAS and CMS analyses of the LHC Run 1
pp data. The data were consistent with the SM predictions. [19].
This thesis also presents a search for additional heavy scalar resonances in the
four-lepton final state, using similar event selection criteria as used in the SM Higgs
boson observation. The search uses 36.1 fb−1 of pp collision data collected with the
ATLAS detector during 2015 and 2016 at a center-of-mass energy of 13 TeV. The
search looks for a peak structure on top of the SM background in the four-lepton
invariant mass spectrum. With a good mass resolution and relatively low background,
the `+`−`+`− final state is suited to search for narrow resonances in the mass range
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3
200 – 1000 GeV. Final results are interpreted as upper limits on the cross section
times branching ratio for different signal hypotheses. The first hypothesized signal is
a heavy scalar particle under the narrow width approximation (NWA), whose natural
width is set to 4 MeV in the Monte Carlo generation. The heavy scalar is assumed
to be predominately produced by the gluon-fusion and vector boson fusion processes.
As various models also favor a large width resonance, three benchmark models with
a width of 1%, 5% and 10% of the resonance mass are studied. For large-width
hypotheses, the interference between the additional heavy scalar and the SM Higgs
boson as well as the additional heavy scalar and the gg → ZZ continuum background
are taken into account. The results for a NWA signal are combined with those in
the `+`−νν final state to enhance the search sensitivity over the full mass range. The
results presented in this thesis extend previous searches for an additional heavy scalar
using 7 and 8 TeV pp collision data published by ATLAS [20]. Similar results were
also reported by CMS [21].
This thesis is organized as the following: Chapter 2 introduces an overview of
the Standard Model and beyond, providing physics motivations for the two analyses.
The LHC and ATLAS detector are described briefly in Chapter 3. Collision data
and simulated Monte Carlo data are summarized in Chapter 4, followed by the re-
construction of physics objects in ATLAS in Chapter 5. The common aspects in the
two analyses including event triggers, the selection criteria of four-lepton candidates,
the methods of background estimation and the statistical treatment, are summarized
in Chapter 6. The observation of a SM Higgs boson in the `+`−`+`− final state is
presented in Chapter 7 and the search for additional heavy scalars in the `+`−`+`−
final state along with the combination with the results from `+`−νν final state are
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4
presented in Chapter 8. Finally, Chapter 9 gives the conclusion and outlook.
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Chapter 2
The Standard Model and Beyond
2.1 Introduction to the Standard Model
The Standard Model (SM) [6–8] of particle physics describes the interactions of
elementary particles through the strong, weak, and electromagnetic forces. Elementary
particles of half-integer spin are called fermions. Fermions with spin-12
constitute the
visible matter in the universe. These fermions include the charged leptons (e, µ, τ),
their corresponding neutral neutrinos (νe, νµ, ντ ), the quarks (u, d, c, s, t, b), and the
antiparticles of each of the leptons and quarks. Elementary particles with integer spin
are called bosons. Bosons that are mediators of the interactions between elementary
particles are called gauge bosons. The γ, W± and Z bosons are mediators for the
electroweak interactions, and the gluons g are mediators for the strong interactions.
All these known gauge bosons have a spin of 1, therefore they are vector bosons. In
addition, the Higgs boson, which is responsible for the mass of the W and Z bosons,
has a spin of 0. A summary of the SM particles is provided in Figure 2.1.
The Standard Model is a renormalizable [22], locally invariant gauge theory [23]
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Figure 2.1: Elementary particles in the Standard Model, including quarks, leptons,
gauge bosons and the Higgs boson. Their masses, charges and spins are also presented.
Picture is taken from www.wikipedia.com.
based on an SU(3)C ⊗ SU(2)L ⊗ U(1)Y symmetry group. The SU(3)C symmetry
group describes the color symmetry of the strong interaction. The eight generators
of SU(3)C symmetry group correspond to eight color quantum states of the massless
gluon. Quantum chromodynamics (QCD) describes the strong interactions, and was
developed during the 1960s based on the SU(3)C symmetry group [24, 25]. During
that time, the electromagnetic and weak interactions were unified into a local gauge
theory of electroweak interactions based on the SU(2)L ⊗ U(1)Y symmetry group,
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the Glashow-Weinberg-Salam (GWS) electroweak theory [6–8]. The SU(2)L sym-
metry group describes the isospin (I) symmetry of the electroweak interaction with
three generators (Aaµ). The U(1)Y symmetry group, describing the hypercharge Y
(Y = Q−I3, where Q is the electric charge) symmetry of the electroweak interactions,
corresponds to a unitary transformation on a complex 1-dimension vector, with one
generator (Bµ). The four generators of the SU(2)L ⊗ U(1)Y symmetry group corre-
spond to the four gauge bosons. The origin of the masses of these W± and Z bosons
is explained by a mechanism that spontaneously breaks a local gauge symmetry.
2.2 The Higgs mechanism
The problem of giving masses to elementary particles was solved in 1964, first
in a paper by Englert and Brout [1] and later in a series of papers by Higgs [2,3], and
others [4, 26]. These papers demonstrated that spontaneous symmetry breaking of a
local gauge symmetry is gauge invariant: the Higgs mechanism.
Weinberg applied this Higgs mechanism to the leptons [7]. He proposed a scalar
doublet φ ≡(φ+
φ0
)which is a self-interacting SU(2)L complex doublet (four real
degrees of freedom) with hypercharge Y = 12
and isospin I = 12:
V (φ) = m2Φ†Φ + λ(Φ†Φ)2 (2.1)
The λ term describes quartic self-interactions of the scalar fields. When m2 < 0 and
λ > 0, the neutral component of the scalar doublet φ0 acquires a non-zero vacuum
expectation value (VEV) ν, inducing the spontaneous breaking of the SM local gauge
symmetry. The symmetry is still present in the theory; only the vacuum state breaks
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the symmetry. Consequently the W± and Z bosons acquire masses,
m2W± =
g2ν2
4, m2
Z =(g′2 + g2)ν2
4,
where g and g′ are the SU(2)L and U(1)Y gauge couplings. The fermions of the SM
can also acquire masses through their Yukawa interactions with the scalar field. The
discovery of the W± [27, 28] and Z bosons [29, 30] in 1983 using the Super Proton
Synchrotron at CERN provided a strong experimental support on the gauge theory of
the electroweak interactions.
In the Higgs mechanism, of the initial four degrees of freedom of the scalar field,
two are absorbed by the W± gauge bosons, and one by the Z gauge boson. The one
remaining degree of freedom, H, is the physical Higgs boson — a new scalar particle.
Its mass is given by mH =√
2λ ν, where λ is the Higgs self-coupling parameter in
Equation 2.1 and ν is the VEV, about 246 GeV. The quartic coupling λ is a free
parameter in the SM, hence the Higgs mass is not determined. Therefore a direct
search for the SM Higgs boson becomes very challenging, requiring detailed studies of
the Higgs boson properties for a large mass range.
2.3 Higgs boson production and decay mechanisms at the
LHC
The SM Higgs boson production cross sections and decay branching ratios, as
well as their uncertainties, are taken from Ref. [31–34].
Higgs boson production mechanisms In the SM, Higgs boson production at the
LHC mainly occurs through the following processes, listed in order of decreasing cross
section at the Run 1 center-of-mass energies:
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• gluon fusion production gg → H, namely ggF (Fig. 2.2(a));
• vector boson fusion production qq → qqH, namely VBF (Fig. 2.2(b));
• associated production with a W boson, qq → WH, namely WH (Fig. 2.3(a)), or
with a Z boson, pp→ ZH, namely ZH, including a small (∼8%) from gg → ZH
(ggZH) (Figs. 2.3, 2.3(b), 2.3(c)); WH and ZH are collectively named as V H.
• associated production with a pair of top (bottom) quarks, qq, gg → ttH(bbH),
namely ttH or (bbH) (Fig. 2.4).
Table 2.1 provides the cross section of a Higgs boson with mH = 125 GeV for different
production processes at√s = 7 and 8 TeV.
g
g
H
(a)
q
q
q
H
q
(b)
Figure 2.2: Examples of leading-order Feynman diagrams for Higgs boson production
via the (a) ggF and (b) VBF production processes.
For a SM Higgs boson of mass around 125 GeV, the largest contribution of its
total production cross section comes from the ggF process, because of the abundance
of gluons in the protons. The massless gluons would not interact with the Higgs
boson except through quantum loops of massive quarks, such as top or bottom quarks.
Because of the top/bottom quark interference in the loops, the ggF production process
provides sensitivity, although limited, to the relative signs of the Higgs coupling to
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q
q
W,Z
H
(a)
g
g
Z
H
(b)
g
g
Z
H
(c)
Figure 2.3: Examples of leading-order Feynman diagrams for Higgs boson production
via the (a) qq → V H and (b, c) gg → ZH production processes.
q
q
t, b
H
t, b
(a)
g
g
t, b
H
t, b
(b)
g
g
t, b
H
t, b
(c)
Figure 2.4: Examples of leading-order Feynman diagrams for Higgs production via
the qq/gg → ttH and qq/gg → bbH processes.
top and bottom quarks [19]. The ggF production cross section is calculated at up to
next-to-next-to-leading order (NNLO) in QCD corrections [35–41]. Next-to-leading
order (NLO) in electroweak (EW) corrections are applied [42,43], as well as the QCD
soft-gluon re-summations at next-to-next-to-leading logarithmic (NNLL) [44]. These
calculations, which are described in Refs [45–48], assume a factorization between the
QCD and EW corrections. The transverse momentum spectrum of the Higgs boson
in the ggF process follows the HqT calcuation [49], which includes QCD corrections
at NLO and QCD soft-gluon re-summations up to NNLL; the effects of finite quark
masses are also taken into account [50].
The second-largest contribution is from the VBF production process, of which
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Table 2.1: The Standard Model predictions for the Higgs boson production cross
section together with their theoretical uncertainties. The value of the Higgs boson
mass is assumed to be mH = 125 GeV. The uncertainties in the cross sections are
evaluated as the sum in quadrature of the uncertainties resulting from variations of
the QCD scales, parton distribution functions, and αs.
production process Cross section [pb]√s = 7 TeV
√s = 8 TeV
ggF 15.1 ± 1.6 19.3 ± 2.0
VBF 1.22 ± 0.03 1.58 ± 0.04
WH 0.58 ± 0.02 0.70 ± 0.02
ZH 0.34 ± 0.01 0.42 ± 0.02
ttH and bbH 0.24 ± 0.04 0.33 ± 0.05
Total 17.5 ± 1.7 22.3 ± 2.1
cross section is calculated at full QCD and EW corrections up to NLO [51–54] and
approximate NNLO QCD corrections [55]. In the VBF production, the Higgs boson
is produced with two forward, separated and energetic jets, which are usually used
in the experiment to distinguish the events of VBF production process from those of
other production processes.
The next important Higgs production is the V H process, where V stands for a
W± or a Z boson. Their cross sections are calculated up to NNLO in QCD correc-
tions [56–58] and NLO in EW corrections [59], except for the gg → ZH production
process, calculated only at NLO in QCD with a theoretical uncertainty assumed to be
30%. The unique decay products from the associated vector boson are experimentally
used to discriminate the events from the V H processes against those of other produc-
tion processes, or to trigger the Higgs events in some analyses, such as the search for
Higgs boson in the bb decay channel.
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The ttH production process bears a relatively low cross section, but contains
significant physics information because it provides a direct measurement of the top-
Higgs Yukawa coupling. Its cross section is estimated up to NLO QCD [60–64]. The
associated top quark pair further decays to other products, resulting in a complicated
multi-object final state where the correlations of all the decay products are of great
importance. Thus, multivariate techniques are widely used in the search for ttH
production process [65,66].
Higgs boson decay mechanisms The Higgs boson couplings to the fundamental
particles are directly related to their masses. More precisely, the SM Higgs couplings
to fermions are linearly proportional to the fermion masses, whereas the couplings to
vector bosons are proportional to the square of the boson masses. As a result, the
dominant Higgs boson decay mechanisms involve the coupling of Higgs boson to W ,
Z bosons and/or the third or second generation quarks and leptons, depending on the
kinematic accessibility. Figure 2.5(a) shows the branching ratio of each decay mode
for different Higgs boson masses. For a light Higgs boson the dominant decay mode is
the bb final state as the WW , ZZ and tt decay modes are kinematically suppressed.
The branching ratios and the relative uncertainty for a SM Higgs boson with
mH = 125 GeV is shown in Table 2.2. Although the branching ratio of H → ZZ →
`+`−`+`− is very small for a low mass Higgs boson, this decay channel possesses an
excellent mass resolution (1–2% for mH = 125 GeV), and a good signal to background
ratio (about 2 for mH = 125 GeV); thus, it is suitable for the search for a resonance
in the range of 200 and 1000 GeV.
The intrinsic width of a Higgs boson (Γh) predicted by the SM increases dramat-
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Table 2.2: The branching ratios and the relative uncertainty for a SM Higgs boson
with mH = 125 GeV.Decay channel Branching ratio Rel. uncertainty
H → γγ 2.27× 10−3 +5.0%−4.9%
H → ZZ 2.62× 10−2 +4.3%−4.1%
H → ZZ → `+`−`+`− (` is e or µ) 1.40× 10−4 +4.3%−4.1%
H → W+W− 2.14× 10−1 +4.3%−4.2%
H → τ+τ− 6.27× 10−2 +5.7%−5.7%
H → bb 5.84× 10−1 +3.2%−3.3%
H → Zγ 1.53× 10−3 +9.0%−8.9%
H → µ+µ− 2.18× 10−4 +6.0%−5.9%
ically when its mass increases, as shown in Figure 2.5(b). At a mass of 1 TeV, its width
is about 600 GeV, which is too large to form a proper resonance. In the search for
additional heavy scalars, the intrinsic width of a heavy scalar is customarily assumed
to be negligibly small comparing to detector resolution, dubbed as the narrow width
approximation (NWA); or it is set to a benchmark width, such as 1%, 5% or 10% of
its mass.
2.4 Two Higgs Doublet Model
The two Higgs doublet model is motivated as shown in Ref. [67]. The best
known one is from the supersymmetry [68] (SUSY). Supersymmetric theories require
at least two scalar fields in order to give masses simultaneously to the charge 23
and
charge −13
quarks (i.e. up-like and down-like quarks). The two Higgs doublet model
assumes there are two Higgs fields (Φ1 and Φ2), each with four degrees of freedom,
hyperchange Y = 12
and isospin I = 12; consequently the potential energy term of
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[GeV]HM90 200 300 400 1000
Hig
gs B
R +
Tota
l U
ncert
410
310
210
110
1
LH
C H
IGG
S X
S W
G 2
01
3
bb
ττ
µµ
cc
gg
γγ γZ
WW
ZZ
(a) branching ratio
[GeV]HM
100 200 300 1000
[G
eV
]H
Γ
210
110
1
10
210
310
LH
C H
IGG
S X
S W
G 2
01
0
500
(b) total width
Figure 2.5: (a) shows the branching ratio of different Higgs decay modes for different
Higgs boson masses. The theoretical uncertainties are shown as bands. (b) shows the
total width of a SM Higgs boson as a function of the Higgs mass hypothesis.
Equation 2.1 becomes:
V = m211Φ†1Φ1 +m2
22Φ†2Φ2 −m212(Φ†1Φ2 + Φ†2Φ1)
+λ1
2(Φ†1Φ1)2 +
λ2
2(Φ†2Φ2)2 + λ3Φ†1Φ1Φ†2Φ2
+ λ4Φ†1Φ2Φ†2Φ1 +λ5
2
[(Φ†1Φ2)2 + (Φ†2Φ1)2
] (2.2)
where all the parameters are real. The minimization of this potential results in two
vacuum expectation values (VEVs): ν1 and ν2. As described in the Higgs mechanism,
the non-zero VEVs spontaneously break the electroweak gauge symmetry. In total
there are eight degrees of freedom in the two scalar fields, of which three are absorbed
by the W± and Z boson just as in the Standard Model. There are five remaining
degrees of freedom — five Higgs bosons: two CP-even Higgs bosons, denoted as H
and h, where h could be the discovered Higgs boson at 125 GeV and the H is assumed
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to be heavier than the h; two charged Higgs bosons (H±) and one CP-odd Higgs boson
(A). There are eight independent parameters of interest:
(a) the mass of the Higgs bosons: mH , mh, mA, and mH± .
(b) the mixing angle between the two CP-even Higgs bosons, α.
(c) the ratio of the vacuum expectation value of the two doublets, tan β = ν1/ν2.
(d) the m12 parameter of the potential.
mh is set to 125 GeV to agree with the observed Higgs boson. It is assumed that other
Higgs bosons (mA, mH±) are heavy enough so that the heavy CP-even Higgs boson,
H, does not decay to them. The cross sections and branching ratios are calculated at
next-to-next-to-leading order with the SusHi and 2HDMC programs [39,42,69–73].
The two Higgs doublets Φ1 and Φ2 can couple to leptons and up- and down-
type quarks in four different types [67]. Since the ZZ final state has no sensitivity
to the coupling of the Higgs boson to leptons, only Type-I and Type-II models are
discussed. In the Type-I model, Φ2 couples to all quarks and leptons, while Φ1 does
not couple to SM particles. In the Type-II model, Φ2 couples to only up-type quarks,
while Φ1 couples to down-type quarks and leptons. In Type-I and Type-II models,
the coupling of the heavy CP-even Higgs boson H to vector bosons is proportional to
cos(β−α). In the limit of cos(β−α)→ 0 the lighter CP-even Higgs boson h becomes
indistinguishable from the observed SM Higgs boson.
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Chapter 3
The LHC and ATLAS detector
3.1 The LHC
The Large Hadron Collider (LHC) at the European Organization for Nuclear
Physics (CERN) is the world’s largest and most powerful particle accelerator. It
consists of a particle accelerator located in a 27 kilometers long circular channel, 100
meters beneath the France-Switzerland border near Geneva, Switzerland. LHC’s first
research run took place from 30 March 2010 to 13 February 2013 at an initial energy
of 3.5 TeV per beam (equally, center-of-mass-energy√s = 7 TeV), which was raised
to 4 TeV per beam (√s = 8 TeV) in 2012 and stayed at 6.5 TeV per beam (
√s = 13
TeV) in 2015 and 2016. The proton–proton (pp) collisions produced by the LHC at
center-of-mass-energies of 7 and 8 TeV during 2011 and 2012 are collectively named as
the LHC Run 1 data set, and those at√s = 13 TeV during 2015 and 2016 are named
as the LHC Run 2 data set in this thesis.
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Hadronic cross section Scattering process at the LHC can be classified as either
hard or soft. Quantum Chromodynamics (QCD) is the underlying theory for all such
processes, but the approach and level of understanding is very different for the two
cases. For hard processes, such as Higgs production, its partonic cross section (σ)
can be predicted with good precision using perturbation theory. For soft processes,
such as underlying events, the rates and event properties are dominated by non-
perturbative QCD effects, which are less well understood. Using the QCD factorization
theorem [74], the hadronic cross section for a general gluon-initiated production of a
particle X (pp→ X) at LHC, as an example, can be formulated as:
σpp→X =
∫dx1fg/p(x1, µ
2F )
∫dx2fg/p(x2, µ
2F )σ(x1p1, x2p2, µ
2R, µ
2F )
where x1 and x2 is the fractional momentum of gluon over the incoming protons; p1
and p2 are the momentum of incoming protons; µF is the factorization scale, which is
the scale that separates hard and soft processes, and µR is the renormalization scale
for the QCD running coupling αs; µF and µR, collectively named as QCD scales, are
usually set to a common value; fg/p is the parton distribution function of gluon with a
momentum fraction of x measured in the momentum transfer of µF . The parton distri-
bution functions, encoding information about the proton’s deep structure, are obtained
from fitting deep inelastic scattering structure function data and then evolved with
the DGLAP equations [75] as a function of energy scales to meet the needs of higher
energy at the LHC. The parton cross section σ of a hard process can be calculated
with perturbative QCD (pQCD) at different orders of αs, thanks to the asymptotic
freedom of the QCD [76]. However, other than in simplest cases, the hadronic cross
sections are calculated automatically with programs such as MadGraph [77].
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Luminosity The luminosity L of a pp collider can be expressed as
L = Rinel/σinel (3.1)
where Rinel is the rate of inelastic collisions and σinel is the pp inelastic cross-section.
For a storage ring, operating at a revolution frequency fr and with nb bunch pairs
colliding per revolution, this expression can be rewritten as
L = (µnbfr)/σinel (3.2)
where µ is the average number of inelastic interactions per bunch crossing. The def-
inition in Equation 3.1 and 3.2 is also referred to as instantaneous luminosity and is
usually expressed in units cm−2s−1. As running conditions vary with time, the lu-
minosity of a collider also has a time dependence. The integral over time is called
integrated luminosity, which is commonly denoted with L =∫Ldt, and measured in
units b−1. One further distincts delivered integrated luminosity, which refers to the
integrated luminosity which the LHC has delivered to an experiment, and recorded in-
tegrated luminosity, which refers to the amount of data that has actually been stored
to disk by the experiment. The delivered luminosity can be written in terms of the
LHC parameters as:
L =nbfrn1n2
2πΣxΣy
(3.3)
where n1 and n2 are the number of protons per bunch in beam 1 and beam 2 respec-
tively, and Σx and Σy characterize the horizontal and vertial convolved beam widths,
which could be directly measured using dedicated bean-separation scans, also known
as van der Meer (vdM) scans [78, 79]. Details of the determination of the luminosity
in pp collision using the ATLAS detector at the LHC can be found at Ref [80–82].
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Some parameters The LHC is designed to collider two proton beams head-by-
head, each of the two beams consisting of 2800 bunches of protons per revolution
and each bunch containing about 1.25 × 1011 protons, with the revolution frequency
of the beam fr about 11.2 kHz. Furthermore the inelastic cross section is about 80
micro-barn (mb) at 8 TeV, and about 100 mb at 13 TeV 1. And the average number of
inelastic interactions per bunch crossing reported by ATLAS for the LHC Run 1 and
Run 2 data sets are shown in Figure 3.1.
Mean Number of Interactions per Crossing
0 5 10 15 20 25 30 35 40 45
/0.1
]1
Record
ed L
um
inosity [pb
0
20
40
60
80
100
120
140
160
180 Online LuminosityATLAS
> = 20.7µ, <1Ldt = 21.7 fb∫ = 8 TeV, s
> = 9.1µ, <1Ldt = 5.2 fb∫ = 7 TeV, s
Mean Number of Interactions per Crossing
0 5 10 15 20 25 30 35 40 45 50
/0.1
]-1
Del
iver
ed L
umin
osity
[pb
0
20
40
60
80
100
120
140
160
180
200=13 TeVsOnline, ATLAS -1Ldt=33.5 fb∫
> = 13.7µ2015: <> = 24.2µ2016: <> = 22.9µTotal: <
7/16 calibration
Figure 3.1: The luminosity-weighted distribution of the mean number of interactions
per bunch crossing for the 2011 and 2012 pp collision data (left), and 2015 and 2016
pp collision data (right).
Pileup Due to the high instantaneous luminosity, as well as the small separation
between collisions, multiple interactions can happen in one single event. Figure 3.1
shows the luminosity-weighted distribution of the mean number of interactions per
bunch crossing for LHC Run 1 and Run 2 data. This effect is collectively called
pileup, and is generated in two forms: (1) In-time pileup: Multiple pp collisions
11mb = 10−3 b, 1 b = 10−24 cm2.
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in the same bunching crossing. Usually collisions associated with the most energetic
physics objects are of physics interest, while others add additional soft energy that
must be corrected for. This type of pileup directly relates to the average number of
interactions per bunch crossing, µ. The larger the µ is, the stronger the in-time pileup
is. (2) Out-of-time pileup: Electronic signals from previous bunch crossing still
present in the detector, causing this effect. For example, the LAr calorimeters signal
length is approximately 500 ns, compared to the bunch spacing of 50 ns in Run 1
data set. Lots of efforts are dedicated to mitigate the pileup effects in the particle
reconstruction and identification.
3.2 The ATLAS detector
A Toroidal LHC Apparatus (ATLAS) is a multi-purpose detector with a forward-
backward symmetric cylindrical geometry and a solid angle 2 coverage of nearly 4π. A
detailed description of the ATLAS detector can be found in Ref. [83]. Figure 3.2 shows
the overall view of the ATLAS detector. Its dimensions are 25 m in height and 44 m
in length. The overall weight is approximately 7000 tonnes. The ATLAS detector
consists of three sub-detectors: inner detector, calorimeter and muon spectrometer.
2ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point
(IP) in the center of the detector and the z-axis along the beam pipe. The x-axis points from the IP
to the center of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used
in the transverse plane, φ being the azimuthal angle around the z-axis. The pseudorapidity is defined
in terms of the polar angle θ as η = − ln tan(θ/2). Distance between two particles are quantified by
∆R =√
∆η2 + ∆φ2, where ∆η is the difference of the two particles in η, and ∆φ is the difference in
φ.
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Figure 3.2: Cut-away view of the ATLAS detector. Its dimensions are 25 m in height
and 44 m in length. The overall weight is approximately 7000 tonnes.
3.2.1 Inner detector
The inner detector, shown in Figure 3.3, immersed in a 2 T magnetic field,
provides precision measurements of the tracks left by electrically charged particles
traversing through the magnetic field. It has complete azimuthal coverage in the range
|η| < 2.5. It is composed by a pixel detector, a silicon strip detectors (SCT) and a
transition radiation trackers (TRT). The pixel detector measures the x, y, z coordinates
of the passed charged particle; the SCT, with pairs of single-sided sensors glued back-
to-back, provides 8 hits per track; and the TRT provides 35 hits per track on-average
in the range |η| < 2.0. The innermost pixel layer, usually dubbed as B-layer, is of
particular importance in finding hadronized bottom quarks and in rejecting converted
photons from real electrons. After the long shutdown during 2014, a Insertable B-layer
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(IBL) [84] was added between beam pipe and the original B-layer as a fourth layer to
the pixel detector at a mean radius of 3.2 cm. The IBL offers better track and vertex
reconstruction performance at the higher luminosity in Run 2 and mitigates the impact
of radiation damage to the original innermost layer. It also improves the resolution of
primary vertex finding 3 by 28% and the uncertainty on the impact parameter by 25%.
Consequently, the rejection of light jets in the tt events for a B-hadron efficiency of
60% is increased by 1.9. The overall tracking performances can be found in Ref. [85].
In general the inner detector provides precision measurements of the momentum of
charged particles with a decent resolution: σ/pT = 0.05% pT ⊕ 1%, where pT is the
particle’s momentum in the unit GeV.
3.2.2 Calorimeters
Outside of the inner detector are the electromagnetic and hadronic calorimeters,
which have complete azimuthal coverage in the range |η| < 4.9. In the central bar-
rel, a high-granularity liquid-argon (LAr) electromagnetic sampling calorimeter with
lead absorbers is surrounded by a hadronic sampling calorimeter (Tile) with steel ab-
sorbers and active scintillator tiles. The LAr technology is also used in the calorime-
ters in endcap, with fine granularity and lead absorbers for EM showers, and with
reduced granularity and copper absorbers for hadronic showers. Solid angle coverage
is completed with forward copper/LAr and tungsten/LAr calorimeter modules (FCal)
that are optimized for electromagnetic and hadronic measurements respectively. Fig-
ure 3.4 shows a cut-view of these calorimeters. To achieve a high spatial resolution,
the calorimeter cells are arranged in a projective geometry with fine segmentation
3The primary vertex is defined as the vertex with the highest sum of pT of tracks associated to it
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Figure 3.3: Drawing shows the sensors and structural elements traversed by a charged
track of 10 GeV in the barrel inner detector (the red line).
in φ and η. Each calorimeters is then longitudinally segmented into multiple layers,
capturing the shower development in depth. In both EM and Tile calorimeters, most
of the absorbers are in the second layer, while in the hadronic endcap, absorbers are
more evenly spread between layers. In the region |η| < 1.8, a pre-sampler detector is
used to correct for the energy lost of electrons and photons due to upstream materials
of the calorimeter.
Radiation length, which is the mean distance over which a high-energy electron
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loses all but 1/e of its energy, and 79
of the mean free path for pair production by a high-
energy photon, is an appropriate scale length for describing the size of EM calorimeter.
The EM calorimeter is over 22 radiation lengths in depth, ensuring that there is little
leakage of EM showers into the hadronic calorimeter. Similarly, interaction length,
which is the mean path length required to reduce the numbers of relativistic charged
particles by the factor 1/e, is used to describe the size of hadronic calorimeters. The
total depth of hadronic calorimeters is over 9 interaction lengths in the barrel and
over 10 interaction lengths in the endcap, achieving a good containment of hadronic
shower. When a hadronic shower is not completely contained, signals in the muon
spectrum are then used to correct the energy of the hadronic shower.
The resolution of measured energy in EM calorimeter is very good:
σ
E=
10%√E⊕ b
E⊕ 0.7%
where b comes from electronic noise of calorimeter, is about 250 MeV. The resolution
of measured energy in hadronic calorimeter is: σ/E = 50%/√E ⊕ 3%.
3.2.3 Muon spectrometer
The muon spectrometers (MS) surround the calorimeters and are the outermost
ATLAS sub-detectors. A system of three large superconducting air-core toroidal mag-
nets generates a magnetic field providing 1.5 to 5.5 Tm of bending power in the barrel
and 1 to 7.5 Tm in the end-cap. Resistive Plate Chambers (RPC, three doublet lay-
ers in the barrel) and Thin Gap Chambers (TGC, three triplet and doublet layers
in the end-caps) constitutes the muon trigger system for the range |η| < 1.05 and
1.0 < |η| < 2.4, respectively, with a time resolution on the order of 1 ns. They also
give (η, φ) position measurements with typical spatial resolutions of 5 – 10 mm up
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Figure 3.4: Cut-away view of the ATLAS calorimeter system. The electromagnetic
(EM) calorimeter is a sampling liquid-argon (LAr) calorimeter with lead absorbers.
The hadronic calorimeter is a sampling calorimeter with steel absorbers and active
scintillator tiles in the barrel and with copper absorbers and LAr scintillator in the
end-cap. The forward calorimeter (FCal) consists of copper/LAr and tungsten/LAr.
to |η| ≈ 2.65, and timing measurements in the non-bending transverse plane. Fur-
thermore, three layers of Monitored Drift Tube chambers (MDT) provide precision
momentum measurements of muons with pseudorapidity up to |η| = 2.7. Each MDT
chamber typically has six to eight η measurements along the muon track with a single
hit resolution in the precision (rz bending) plane of about 80 µm. For |η| < 2, the in-
ner layer is instrumented with a quadruplet of Cathode Strip Chambers (CSC) instead
of MDTs. CSC detectors measure position in rz plane with a single hit resolution of
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about 60 µm and provide a time measurement with a resolution of 3.6 ns. The relative
resolution of measured muon momentum is better than 3% over a wide pT range and
up to 10% at pT = 1 TeV.
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Chapter 4
Data and Monte Carlo samples
4.1 Data samples
The observation of the SM Higgs boson uses pp collision data collected by the
ATLAS detector during 2011 and 2012 at center-of-mass energies of√s = 7 and
8 TeV with a bunch spacing of 50 ns. Only events taken in stable beam conditions,
and in which the trigger system, the tracking devices, the calorimeters and the muon
chambers were functioning as expected, are considered in the physics analysis. The
resulting effective luminosity for 7 TeV pp data is 4.5 fb−1, and for 8 TeV pp data is
20.3 fb−1. The overall uncertainty on the integrated luminosity for the complete 2011
data set is ±1.8% [86]. The uncertainty on the integrated luminosity for the 2012 data
set is ±2.8%; this uncertainty is derived following the methodology used in the 2011
data set, from a preliminary calibration of the luminosity scale with beam-separation
scans [78,79] performed in November 2012.
The search for additional heavy scalars uses the pp collision data collected by the
ATLAS detector in 2015 and 2016 at a center-of-mass energy of√s = 13 TeV with a
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bunch spacing of 25 ns. The effective integrated luminosity used in the physics analysis
for 2015 and 2016 data set is 36.1 fb−1. The uncertainty on the integrated luminosity
of 2015 and 2016 data set is ±3.2%. This is derived , following a methodology similar
to that detailed in Ref. [82], from a preliminary calibration of the luminosity scale
using x-y beam separation scans performed in May 2016.
4.2 Monte Carlo samples
4.2.1 Overview
The ATLAS simulation software chain [87] is generally divided into three steps:
(1) the generation of the event for immediate decays, which can be carried out by
different generators, following the Les Houches Event file format [88]; (2) the simu-
lation of the detector and soft interactions within the GEANT4 framework [89, 90];
and (3) the digitization of the energy deposited in sensitive regions of the detector
into voltages and currents for comparison to the readout of the ATLAS detector. The
output of the simulation chain can be presented in a format identical to the output of
the ATLAS data acquisition system (DAQ). Thus, both the simulated and observed
data can then be run through the same ATLAS trigger and physics reconstruction
packages.
In each step, intermediate files are produced and named differently. Files from
event generation are usually named as EVNT, in which information called “truth”
is recorded for each event. The truth information is a history of the interactions
from the generator, including incoming and outgoing particles. A record is kept for
every particle, whether the particle is to be passed through the detector simulation
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or not. Files from the simulation of the ATLAS detector are named as HITS, which
are then treated as the inputs of the digitization together with additional simulated
HITS files for minimum bias, beam halo, beam gas and cavern background events .
These additional simulated HITS files are used to mimic the underlying soft events,
particularly the minimum bias files that simulate the “pileup events”, which become
more important as the instantaneous luminosity increases. The Monte Carlo (MC)
generator used for pileup events is Pythia 8.212 [91] with either the A14 [92] set
of tuned parameters and NNPDF23 [93] for the parton density functions (PDF) set,
or the AZNLO [94] tuned parameters and CTEQL1 [95] PDF when the Powheg-
Box [96,97] generator is used for the hard process. The simulated events are weighted
to reproduce the observed distribution of the mean number of interactions per bunch
crossing in the data (pileup reweighting). The properties of the bottom and charm
hadron decays are simulated by the EvtGen v1.2.0 program [98].
4.2.2 Signal Monte Carlo samples
The SM Higgs boson signal is modeled using the Powheg-Box generator [96,97,
99,100], which calculates separately the gluon-gluon fusion and weak-boson fusion pro-
duction with matrix elements up to next-to-leading order (NLO) in the QCD coupling
constant. The Higgs boson transverse momentum (pT) spectrum in the ggF process is
re-weighted to follow the calculation of Ref. [101,102], which include QCD corrections
up to next-to-next-to-leading order (NNLO) and QCD soft-gluon resummations up
to next-to-next-to-leading logarithm (NNLL). The effects of non-zero quark masses
are also taken into account [50]. Powheg-Box is interfaced to Pythia 8 [91, 103]
for showering and hadronization, which in turn is interfaced to Photos [104, 105]
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for QED radiative corrections in the final state. Pythia 8 is used to simulate the
production of a Higgs boson in associated with a W or a Z boson (VH) or with a tt
pair (ttH). The production of a Higgs boson in association with a bb pair (bbH) is
included in the signal yield assuming the same mH dependence as for the ttH process,
while the signal efficiency is assumed to be equal to that for ggF production.
In the search for additional scalars, heavy scalar events are produced using
the Powheg [99, 100] generator, which calculates separately the gluon-gluon fusion
and vector boson fusion production with matrix elements up to next-to-leading order
(NLO) in the QCD coupling constant. The generated events then are interfaced to
Pythia 8 [91,103] for decaying the Higgs boson into the four-lepton final state as well
as for showering and hadronization. Events from ggF and VBF production are gener-
ated separately in the 200 < mH < 1400 GeV mass range under the NWA. In addition,
events from ggF production with a width of 15% of the scalar mass mH have been
generated with MadGraph5 aMC@NLO [77,106] to validate the signal modeling for
LWA. To have better description of the jet multiplicity, MadGraph5 aMC@NLO is
also used to generate the events of pp→ H+ ≥ 2 jets at NLO QCD accuracy with the
FxFx merging scheme [107], in the Effective Field Theory (EFT) approach (mt →∞).
The fraction of the ggF events that enter into the VBF-like category is estimated from
MadGraph5 aMC@NLO simulation.
4.2.3 Background Monte Carlo samples
The ZZ(∗) continuum background from qq annihilation is simulated with Sherpa
2.2 [108–110], with the NNPDF3.0 [111] NNLO PDF set for the hard scattering pro-
cess. NLO accuracy is achieved in the matrix element calculation for 0-, and 1-jet final
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states and LO accuracy for 2- and 3-jet final states. The merging of jets from the hard
process and parton shower is performed with the Sherpa parton shower [112] using
the MePs@NLO prescription [113]. NLO EW corrections are applied as a function of
mZZ [114,115]. The EW production of vector boson scattering with two jets down to
O(α6W ) is generated using Sherpa, where the process ZZZ → 4`qq is also taken into
account.
The gg → ZZ(∗) production is modeled by Sherpa 2.2 at LO in QCD, including
the off-shell h contribution and the interference between h and the ZZ background.
The k-factor accounting for higher order QCD effects for the gg → ZZ(∗) continuum
production has been calculated for massless quark loops [116–118] in the heavy top-
quark approximation [119], including the gg → H∗ → ZZ processes [120]. Based on
these studies, a k-factor of 1.7 is used, and a conservative relative uncertainty of 60%
on the normalization is applied to both searches.
The WZ background is modeled using POWHEG-BOX v2 interfaced to
PYTHIA 8 and EvtGen v1.2.0. The triboson backgrounds ZZZ, WZZ, and WWZ
with four or more prompt leptons are modeled using Sherpa 2.1.1. For the fully lep-
tonic tt+Z background, with four prompt leptons coming from the top and Z decays,
MadGraph5 aMC@NLO is used.
Events containing Z bosons with associated jets are simulated using the Sherpa
2.2.0 generator. Matrix elements are calculated for up to 2 partons at NLO and 4 par-
tons at LO using the Comix [109] and OpenLoops [110] matrix element generators
and merged with the Sherpa parton shower [112] using the ME+PS@NLO prescrip-
tion [113]. The CT10 PDF set is used in conjunction with dedicated parton shower
tuning developed by the Sherpa authors. The Z + jets events are normalized to the
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NNLO cross sections.
The tt background is modeled using POWHEG-BOX v2 interfaced to PYTHIA
6 [121] for parton shower, fragmentation, and the underlying event and to EvtGen
v1.2.0 for properties of the bottom and charm hadron decays.
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Chapter 5
Object Reconstruction and Identification
The four-lepton channel has a small event rate but is a relatively clean final state where
the signal-to-background ratio, taking the reducible backgrounds into account alone,
i.e. ignoring the ZZ background, is above 6 in the observation of a SM Higgs boson
analysis; the search for additional heavy scalars in high-mass regions is background
free for m4` > 400 GeV. Significant effort was made to obtain a high efficiency for the
reconstruction and identification of electrons and muons, while keeping the loss due
to background rejection as small as possible. In particular, this becomes increasingly
difficult for electrons as ET decreases.
Electrons are reconstructed using information from the ID and the electromag-
netic calorimeter. For electrons, background discrimination relies on the shower shape
information available from the highly segmented LAr EM calorimeter, high-threshold
TRT hits, as well as compatibility of the tracking and calorimeter information. Muons
are reconstructed as tracks in the ID and MS, and their identification is primarily based
on the presence of a matching track or tag in the MS. Finally, jets are reconstructed
from clusters of calorimeter cells and calibrated using a dedicated scheme designed
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to adjust the energy measured in the calorimeter to that of the true jet energy on
average.
5.1 Electron reconstruction and identification
Electron Reconstruction Electron reconstruction in the central region of the AT-
LAS detector (|η| < 2.47) starts from energy deposits (seed-clusters) in the EM
calorimeter that are matched to reconstructed tracks of charged particles in the in-
ner detector. The η–φ space of the EM calorimeter system is divided into a grid of
Nη ×Nφ = 200× 256 towers of size ∆ηtower ×∆φtower = 0.025× 0.025, corresponding
to the granularity of the EM accordion calorimeter middle layer. The energy of the
calorimeter cells in all longitudinal-depth layers is summed to get the tower energy.
Seed clusters of towers with total transverse energy above 2.5 GeV are searched for
using a sliding-window algorithm. For each seed cluster passing loose shower-shape
requirements, a region-of-interest is defined as a cone of size ∆R = 0.3 around the
seed cluster barycenter. An electron is reconstructed if at least one track is matched
to the seed cluster. To improve reconstruction efficiency for electrons that undergo
significant energy loss due to bremsstrahlung, the track associated to the seed cluster
is refitted using a Gaussian-Sum Filter [122]. The electron reconstruction efficiency is
97% for electrons with ET = 15 GeV and 99% at ET = 50 GeV.
Electron Identification Not all objects built by the electron reconstruction algo-
rithms are prompt electrons, which are referred to those coming from W or Z-boson
decays. Background objects include hadronic jets as well as the electrons from con-
verted photon decays, Dalitz decays and semi-leptonic heavy-flavor hadron decays.
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To distinguish signal electrons from background objects, the variables that describe
longitudinal and lateral shapes of the electromagnetic showers in the calorimeters,
the properties of the tracks in the ID and the matching between tracks and energy
clusters are used in a multivariate technique. Out of different multivariate techniques,
the likelihood was chosen for electron identification because of its simple construction.
An overall probability for each object to be signal or background is calculated as:
dL =LS
LS + LB, LS(B)(~x) =
n∏i=1
PS(B),i(xi)
where ~x is the vector of variable values and PS,i(xi) is the value of the signal probability
density function (PDF) of the ith variable evaluated at xi. In the same way, PB,i(xi)
refers to that for the background. These signal and background PDFs are obtained
from data in different |η| and ET bins. By applying a cut on the dL to match the
target signal efficiency expectations, different working points are defined, including
“Loose”, “Medium” and “Tight”. The “Loose” criteria is used in this analysis. An
insertable b-layer hit or, if no such hit is expected, an innermost pixel hit is required
for all electrons. The signal efficiency, including reconstruction and identification, is
measured both in data and MC simulation [123] as a function of the transverse energy
ET and the pseudo-rapidity η as shown in Figure 5.1. The disagreement between
efficiencies obtained in data and the simulated events is around 5%, due to the known
mis-modeling of shower shapes and other identification variables in the simulation.
The ratios of the efficiencies measured in data and simulation (so called “scale factors”)
and their associated uncertainties are used in this analysis to correct the yields of
electrons in simulated events. For electrons with ET < 30 GeV, the total uncertainties
on the efficiencies vary from 1% to 3.5%, dominated by statistical uncertainties. For
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Rec
o +
ID e
ffici
ency
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1ATLAS Preliminary
-1 = 13 TeV, 3.2 fbs
<2.47η-2.47<
Data: full, MC: open
Loose Medium Tight
[GeV]TE
10 20 30 40 50 60 70 80
Dat
a / M
C
0.8
0.9
1R
eco
+ ID
effi
cien
cy
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1ATLAS Preliminary
-1 = 13 TeV, 3.2 fbs
>15 GeVTE
Data: full, MC: open
Loose Medium Tight
η
2.5− 2− 1.5− 1− 0.5− 0 0.5 1 1.5 2 2.5
Dat
a / M
C
0.8
0.9
1
Figure 5.1: Combined electron reconstruction and identification efficiencies in Z → ee
events as a function of the transverse energy ET, integrated over the full pseudo-
rapidity range (left), and as a function of pseudorapidity η, integrated over the full ET
range (right). The data efficiencies are obtained from the data-to-MC efficiency ratios
measured using J/ψ and Z tag-and-probe, multiplied by the MC prediction for elec-
trons from Z → ee decays. The uncertainties are obtained with pseudo-experiments,
treating the statistical uncertainties from the different (ET, η) bins as uncorrelated.
Two sets of uncertainties are shown: the inner error bars show the statistical uncer-
tainty, the outer error bars show the combined statistical and systematic uncertainty.
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electrons with ET > 30 GeV, the total uncertainties are below 1%.
5.2 Muon reconstruction and identification
Muon Reconstruction Muon reconstruction is essentially to reconstruct a track
for the muon. Tracks are first reconstructed independently in the ID and MS, and
then combined to form the muon tracks that are used in physics analyses. Various
algorithms are used to combine MS tracks and ID tracks, resulting in different types
of muons [124,125]:
• Combined (CB) muons: a combined track is formed with a global fit using
the hits from both the ID and MS subdetectors. Most muons are reconstructed
following an outside-in patter recognition, in which the muons are first recon-
structed in the MS and then extrapolated inward and matched to an ID track.
An inside-out combined reconstruction, in which ID tracks are extrapolated out-
ward and matched to MS tracks, is used as a complementary approach.
• Segment tagged (ST) muons: ST muons are used when muons cross only
one layer of MS chambers, failing to form a proper MS track. A track in the ID
is identified as an ST muon if the trajectory extrapolated to the MS is associated
with at least one local track segment in the precision muon chambers.
• Calorimeter tagged (CT) muons: A track in the ID is identified as a CT
muon if it matches to an energy deposit in the calorimeters compatible with a
minimum-ionizing particle. It’s used to recover the efficiency in the region of
|η| < 0.1 where the ATLAS muon spectrometer is only partially instrumented
to allow for cabling and services to the calorimeters and inner detector. The
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CT-muon identification criteria are optimized for a momentum range of 15 <
pT < 100 GeV.
• Extrapolated (ME) muons (SA): the muon track is reconstructed based only
on the MS track and a loose requirement on compatibility with originating from
the interaction point. The parameters of the muon track are defined at the
interaction point, taking into account the estimated energy loss of the muon in
the calorimeters.
Overlaps between different muon types are resolved before producing the collection of
muons used in physics analyses. When two muon types share the same ID track, the
preferred order of the chosen muon is: CB, ST and CT muons.
Muon Identification Muon identification is performed by applying a set of qual-
ity requirements based on the muon types described above. The fake muon mainly
comes from pion and kaon decays. CT and ST muons are restricted to the |η| < 0.1
region while ME muons are allowed only in 2.5 < |η| < 2.7. A set of track quality re-
quirements are applied to the ID tracks to reject poorly reconstructed charged-particle
trajectories. Different MS hit requirements are applied to different muon types. ME
muons are required to have ≥ 3 precision hits (i.e. MDT or CSC hits) in each of the
three layers of the MS. Combined muons are required to have ≥ 3 precision hits in at
least two layers of MDT, except for |η| < 0.1 region where tracks with at least three
hits in one single MDT layer are allowed. To suppress muons produced from in-flight
decays of hadrons, the difference of measured charge-over-momentum between the ID
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and the MS is required to be small:
|q/pID − q/pMS|√σ2
ID + σ2ME
< 7
For muons with |η| < 2.7 and 5 < pT < 100 GeV, the reconstruction and identification
efficiency is above 99% for Run 1 data set [124] and close to 99% for Run 2 data
set [125].
5.3 Jet reconstruction
Jets are reconstructed at the electromagnetic energy scale (EM scale) with the
anti-kt algorithm [126] and radius parameter R = 0.4 using the FastJet software
package [127]. A collection of three-dimensional, massless, positive-energy topological
clusters (topo-clusters) [128, 129] made of calorimeter cell energies are used as input
to the anti-kt algorithm. Topo-clusters are built from neighboring calorimeter cells
containing a significant energy above a noise threshold that is estimated from mea-
surements of calorimeter electronic noise and simulated pileup noise. The topo-cluster
reconstruction algorithm was improved in 2015, particularly preventing topo-clusters
from being seeded by the pre-sampler layers. This restricts jet formation from low-
energy pileup depositions that do not penetrate the calorimeters [130].
Ref. [130, 131] details the methods used to calibrate the four-momentum of jets
in Monte Carlo simulation and in data collected by the ATLAS detector for Run 1 and
Run 2 data sets. The jet energy scale (JES) calibration consists of several consecutive
stages derived from a combination of MC-based methods and in situ techniques. The
MC-based calibrations correct the reconstructed jet four-momentum to that found
from the simulated stable particles within the jet. The calibrations account for features
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of the detector, the jet reconstruction algorithm, jet fragmentation, and the pileup.
In situ techniques are used to measure the difference in jet response between data and
MC simulation, with residual corrections applied to jets in data only.
Fake jets are mainly from beam-induced non-pp collision events [132], cosmic-ray
showers produced in the atmosphere overlapping with collision events, and calorimeter
noise from large scale coherent noise or isolated pathological cells. To remove these
fake jets, the loose jet quality criteria, which are designed to provide an efficiency
of selecting jets from pp collisions above 99.5% (99.9%) for pT > 20(100) GeV, as
described in Ref. [133], are applied. On the other hand, pileup jets, resulting from
multiple pp interactions, are real jets but of no physics interest. They are suppressed
by using the jet-vertex-tagger (JVT) [134], which is a likelihood ratio that is based on
two variables. One variable is the corrected jet-vertex fraction, which is the fraction
of the total momentum of the tracks that are associated with the primary vertex over
the total momentum of the tracks inside the jets. The other one is the RpT, which
is defined as the scalar pT sum of the tracks that are associated wiare icalth the jet
and originate from the hard-scatter vertex divided by the fully calibrated jet pT. The
efficiency of the JVT selecting non-pileup jets is about 97%.
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Chapter 6
Analysis Overview
The observation of the SM Higgs boson and the search for additional scalars in the
four-lepton final state, reported in this thesis, are the same analyses except that (1) the
former focuses on the mass range [110, 140] GeV, while the later searches an resonance
in the mass range [200, 1200] GeV. (2) the former uses the LHC Run 1 data sets,
sometimes called Run 1 Higgs analysis, while the later uses the LHC Run 2 data
sets, sometimes called Run 2 high-mass analysis. Correspondingly, some trigger and
kinematic thresholds were adjusted for the Run 2 analysis, due to the improved object
identifications and the increased instantaneous luminosity. The LHC Run 2 data sets
were also used for the measurements of the observed SM Higgs boson, but only the
results of the measurements are briefly reported in this thesis. (3) the categorization
strategy of the four-lepton candidates are different between the Higgs analysis and the
high-mass analysis. This chapter summarizes common aspects of the two analyses.
Section 6.1 describes the event triggers and Section 6.2 describes the inclusive four-
lepton event selections. The background estimation and statistical methodology are
detailed in Section 6.3 and Section 6.4.
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6.1 Triggers
The LHC has an event rate of 1 GHz (109 Hz) but the maximum bandwidth of
ATLAS is only 100 kHz, so it’s impossible to record all events, and neither is needed.
A trigger is a system that uses simple criteria to rapidly decide which events to keep
when only a small fraction of the total can be recorded. It is the very first step to
distinguish signal events from the backgrounds.
Triggers usually make heavy use of a parallelized design and are divided into
levels. The idea is that each level selects the data that becomes an input for the
following level, which has more time available and more information to make a better
decision. In the ATLAS trigger system, the triggers in the first level are called L1
triggers, which use the customized hardware processors to make an initial decision.
The L1 system suppresses the event rate down to 70 (100) kHz for the Run 1 (Run 2)
data sets, and then delivers accepted events to the next level: High Level Trigger
system (HLT triggers). In the LHC Run 1 data taking, intermediate-level triggers, L2
triggers, was used after the L1 trigger and before the HLT triggers. The HLT system
has access to all detector information of all data and can perform reconstruction and
identification of the physics objects.
Four-lepton events were selected with the single lepton, and dilepton triggers.
The pT (ET) thresholds for single-muon (single-electron) triggers increased from 18 to
24 GeV (20 to 24 GeV) between 7 and (8 and 13 TeV) data, in order to cope with the
increasing instantaneous luminosity. The dilepton trigger thresholds for 7 TeV data are
set at 10 GeV in pT for muons, 12 GeV in ET for electrons and (6, 10) GeV for (muon,
electron) mixed-flavor pairs. For the 8 TeV and 13 TeV data, the thresholds were raised
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to 13 GeV for dimuon trigger, to 12 GeV for the dielectron trigger and (8, 12) GeV for
the (muon, electron) trigger; furthermore, a dimuon trigger with different thresholds
on the muon pT, 8 and 18 GeV, was added. Tri-lepton triggers were introduced in 2015
for the four-lepton analysis in Run 2. Tri-lepton triggers require events fulfill any of
the following criteria: three electrons with ET > 9 GeV and at least one of them with
ET > 17 GeV; or three muons with pT > 6 GeV; or three muons with pT > 4 GeV
and at least one of them with pT > 18 GeV. The trigger efficiency for events passing
the final selection is above 96% in the 4µ, 2µ2e channels and close to 100% in the 4e
and 2e2µ channel for all data sets.
6.2 Inclusive four-lepton event selections
Each event is required to have at least one vertex with two associated tracks
with pT > 400 MeV. As different objects can be reconstructed from the same detector
information, a strategy of removing overlapping objects is applied: for an electron and
a muon that share the same ID track, if the muon is not a CT muon or an ST muon,
the muon is removed otherwise the electron is removed. Also, jets that overlap with
electrons or muons are removed.
Four-lepton candidates are formed by selecting a lepton-quadruplet made out of
two same-flavor, opposite-sign lepton pairs, and classified into three channels based
on the lepton flavors: 4µ, 2e2µ and 4e. Each electron must satisfy ET > 7 GeV and
|η| < 2.47. The crack region (1.37 < |η| < 1.52) is included to prevent acceptance
loss despite the worse resolution in this region of the calorimeter. The fraction of the
events with at least one electron in the crack region is ∼ 18% in the 4e channel and
∼ 9% in the 2e2µ and 2µ2e channels. CT muons are required to have pT > 15 GeV,
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while other types of muons are required to have pT > 6 GeV for the analysis using
the LHC Run 1 data sets (Run 1 analysis) and pT > 5 GeV for the analysis using the
LHC Run 2 data sets (Run 2 analysis). The lower threshold for the Run 2 analysis
provides an increase in the signal acceptance of about 7% in the 4µ final state for the
SM Higgs boson. The three leading leptons, ordered by pT, must have pT larger than
20, 15 and 10 GeV respectively. For each quadruplet at most one CT or ST muon or
muon in the forward region (2.5 < |η| < 2.7) is allowed.
At this point, only one quadruplet per channel is selected, by keeping the quadru-
plet with the lepton pairs closest (leading pair) and second closest (sub-leading pair)
to the pole mass of Z boson, with invariant masses referred to as m12 and m34. In the
selected quadruplet the m12 is required to be 50 < m12 < 106 GeV, while the m34 is
required to be less than 115 GeV and greater than a threshold. The threshold value is
12 GeV for m4` ≤ 140 GeV, rises linearly from 12 to 50 GeV with m4` in the interval
of [140 GeV, 190 GeV] and stays to 50 GeV for m4` > 190 GeV.
To reject leptons from J/Ψ, any same-flavor opposite-charge di-lepton pair is
required to have invariant mass > 5 GeV. The four leptons in the quadruplet are
required to be separated by ∆R > 0.1 for same flavor leptons and ∆R > 0.2 for
different flavor leptons.
The Z+jets and tt background contributions are reduced by applying impact
parameter requirements as well as track- and calorimeter-based isolation requirements
to the leptons. The transverse impact parameter significance, defined as the impact
parameter calculated with respect to measured beam line position in the transverse
plane divided by its uncertainty, |d0|/σd0 , for all muons (electrons) is required to be
lower than 3 (5). The normalized track isolation discriminant, defined as the sum
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of the transverse momenta of tracks inside a cone of size ∆R = 0.3(0.2) around the
muon (electron) candidate, excluding the lepton track, divided by the lepton pT, is
required to be smaller than 0.15. The larger muon cone size corresponds to that used
by the muon trigger. Contributions from pileup are suppressed by requiring tracks
in the cone to originate from the primary vertex. To retain efficiency at higher pT,
the track-isolation requirement is reduced to 10 GeV/pT for pT above 33 (50) GeVfor
muons (electrons).
The relative calorimetric isolation is computed as the sum of the cluster trans-
verse energies ET in the electromagnetic and hadronic calorimeters, with a recon-
structed barycenter inside a cone of size ∆R = 0.2 around the candidate lepton,
divided by the lepton pT. The clusters used for the isolation are the same as those for
reconstructing jets. The relative calorimetric isolation is required to be smaller than
0.3 (0.2) for muons (electrons). The measured calorimeter energy around the muon
and the cells within 0.125×0.175 in η×φ around electron barycenter are excluded from
the respective sums. The pileup and underlying event contribution to the calorimeter
isolation is subtracted event by event [135]. For both the track- and calorimeter-based
isolation requirements any contribution arising from other leptons of the quadruplet
is subtracted.
For the Run 2 analysis, an additional requirement based on a vertex-reconstruction
algorithm, which fits the tracks of the four-lepton candidates under the assumption
that they originate from a common vertex, is applied in order to reduce further the
Z+jets and tt background contributions. A loose cut of χ2/ndof < 6 for 4µ and < 9
for the other channels is applied, which leads to a signal efficiency larger than 99% in
all channels.
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The QED process of radiative photon production in Z boson decays is well mod-
eled by simulation. Some of the final-state radiation (FSR) photons can be identified
in the calorimeter and incorporated into the analysis. The strategy to include FSR
photons into the reconstruction of Z bosons is the same as in Run 1 [136]. It consists
of a search for collinear (for muons) and non-collinear FSR photons (for both muons
and electrons) with only one FSR photon allowed per event. After the FSR correc-
tion, the lepton four-momenta of both di-lepton pairs are recomputed by means of a
Z-mass-constrained kinematic fit. The fit uses a Breit-Wigner Z line shape and a sin-
gle Gaussian per lepton to model the momentum response function with the Gaussian
width set to the expected resolution for each lepton. The Z-mass constraint is applied
to both Z candidates, and improves the m4` resolution by about 15%.
Events that survive these selections are signal Higgs boson candidates. These
events are then classified into different categories to enhance overall search sensitivities,
depending on the analysis under consideration.
6.3 Background estimation
6.3.1 Overview
The non-resonant SM ZZ(∗) continuum process, whose cross section is about 10
times larger than that of H → ZZ(∗), is called the irreducible background, as it pos-
sesses the same final state as the H → ZZ(∗) → `+`−`+`− process. The irreducible
background is modeled by Monte Carlo (MC) simulation with next-to-next-to-leading
order QCD corrections and next-to-leading order electroweak corrections [114,137,138]
applied as a function of the four-lepton invariant mass. The Z+jets, top-quark pair
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and WZ production processes, called reducible backgrounds, enter the four-lepton sig-
nal region via fake leptons, which are reduced by imposing identification requirements.
The reducible backgrounds are important for the observation of the SM Higgs boson
but much less important for the search for additional scalars, as they populate mainly
the low mass region. The rate of these reducible backgrounds entering the signal
region is very low, requiring many simulated events in order to have small statisti-
cal uncertainties. To cope with this, data-driven methods are employed to estimate
the reducible backgrounds. Minor contamination from tri-bosons and leptonic decay
channels of tt +Z is modeled by MC simulation.
The reducible backgrounds are estimated separately for the ``+ ee and ``+ µµ
channels, where `` are the two leptons (e or µ) coming from the leading Z-boson,
via data-driven methods that follow a general procedure: (a) define control regions
(CRs) that target different fake backgrounds by relaxing or inverting isolation/impact
parameter significance criteria and/or lepton identification requirements; (b) study
background compositions and shapes in these CRs, (c) measure efficiencies for each
background source in these CRs or in additional other control regions. (d) extract
background events in the signal region from the CRs via transfer factors, which are
calculated from MC simulation with corrections that account for the differences be-
tween MC simulation and data.
6.3.2 ``+ µµ background
The `` + µµ reducible background arises mainly from three components: the
semileptonic decays of Z+heavy-flavor (HF) jets, the in-flight decays of Z+light-flavor
(LF) jets, and the decays of tt process. A reference control region that is enriched in
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the three components with good statistics is defined by applying the analysis event
selections, except for the isolation and impact parameter requirements that are applied
on the two muons in the subleading dilepton pair. The number of events for each
background component in the reference control region is estimated from an unbinned
maximum likelihood fit, performed simultaneously to four orthogonal control regions,
each of them providing information on one or more of the background components.
Finally, the background estimates in the reference control region are extrapolated to
the signal region via MC-based transfer factors.
The control regions used in the maximum likelihood fit are designed to be or-
thogonal and to minimize the contamination from the Higgs boson signal and the ZZ(∗)
background. The four control regions are:
1. Inverted criteria on impact parameter significance. Candidates are se-
lected following the standard analysis selections, but (1) without applying the
isolation requirement to the muons of the subleading dilepton and (2) requiring
that at least one of the two muons fails the impact parameter significance se-
lection. For the Run 2 analysis, the vertex requirement is not applied to gain
statistics. As a result, this control region is enriched in the Z+HF and tt events.
2. Inverted criteria on isolation: Candidates are selected following the standard
analysis selections, but requiring that at least one of the muons of the subleading
dilepton fails the isolation requirement. For the Run 2 analysis, the vertex cut
is applied to reject the contamination from Z+HF and tt. This control region is
enriched in the Z+LF events and tt events.
3. eµ leading dilepton (eµ+µµ): Candidates are selected following the standard
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analysis selections, but requiring the leading dilepton to be an electron-muon
pair. For the Run 2 analysis, the vertex requirement is not applied. Moreover,
the impact parameter and isolation requirements are not applied to the two
muons of the subleading dilepton. This control region is dominated by tt events.
4. Same-sign (SS) subleading dilepton: Candidates are selected following the
standard analysis selections, but for the subleading dilepton neither isolation nor
impact parameter significance requirements are applied and the two muons are
required to have the same charge (SS). This SS control region is not dominated
by a specific background.
The residual contributions from ZZ(∗) and WZ production are estimated for each con-
trol region from MC simulation. In the unbinned likelihood fit, the observable is the
invariant mass of the leading dilepton pair (m12), which peaks at the Z mass for the
Z+jets events and has a broad distribution for the tt events. The m12 distribution
is parameterized by a second-order Chebyshev polynominal for the tt events and a
Breit-Wigner function convolved with a Crystal Ball function for the Z+jets events.
The parameters of these functions are derived from simulation with MC statistic un-
certainties implemented as nuisance parameters. The results of the combined fit in the
four control regions are shown in Figure 6.1 for the Run 1 data sets and in Figure 6.2
for the Run 2 data sets, along with the individual background components, while the
event yields in the reference control region are summarized in Table 6.1.
Finally the estimated number of events for each contribution in the reference
control region is extrapolated to the signal region by multiplying each background
component by the probability of satisfying the isolation and impact parameter signif-
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Table 6.1: Data-driven `` + µµ background estimates for the Run 1 and Run 2 data
sets, expressed as yields in the reference control region, for the combined fits of four
control regions. The statistical uncertainties are also shown.Z+heavy-flavor jets Z+light-flavor jets Total Z+jets tt
Run 1 159 ± 20 49 ± 10 208 ± 22 210 ± 12
Run 2 908 ± 52 50 ± 21 958 ± 57 918 ± 23
icance requirements, estimated from the relevant simulated samples. The systematic
uncertainty in these transfer factors stems mostly from the size of the simulated MC
samples. It is 6% for Z+heavy-flavor jets, 60% for Z+light-flavor jets and 16% for tt for
the Run 1 analysis; and it is 12% for Z+heavy-flavor jets, 70% for Z+light-flavor jets,
and 10% for tt for the Run 2 analysis. Furthermore, these simulation-based transfer
factors are validated with data using muons accompanying Z → `` candidates, where
the leptons composing the Z boson candidate are required to satisfy isolation and
impact parameter criteria. Events with four leptons, or with an opposite-sign dimuon
with mass less than 5 GeV, are excluded. Based on the data/simulation agreement
of the efficiencies in this control region, an additional systematic uncertainty of about
2% is added for the Run 1 analysis. For the Run 2 analysis, the mismodeling of the
efficiency of isolation for a light-flavor jet in simulation is observed, resulting in a
conservative 100% systematic uncertainty for the Z+light-flavor jets.
The reducible background estimates in the signal region in the full m4` mass
range are given in Table 6.2, separately for the√s = 7 TeV, 8 TeV and 13 TeV data.
The uncertainties are separate into statistical and systematic contributions, where
in the latter the transfer factor uncertainty and the fit systematic uncertainty are
included.
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Table 6.2: Estimates for the `` + µµ background in the signal region for the full
m4` mass range for the√s = 7 TeV, 8 TeV and 13 TeV data. The Z+jets and tt
background estimates are data-driven and the WZ contribution is from simulation.
The statistical and systematic uncertainties are presented in a sequential order. The
statistical uncertainty for the WZ contribution is negligible.4µ 2e2µ√
s = 7 TeV
Z+jets 0.42 ± 0.21 ± 0.08 0.29 ± 0.14 ± 0.05
tt 0.081 ± 0.016 ± 0.021 0.056 ± 0.011 ± 0.015
WZ 0.08 ± 0.05 0.19 ± 0.10√s = 8 TeV
Z+jets 3.11 ± 0.46 ± 0.43 2.58 ± 0.39 ± 0.43
tt 0.51 ± 0.03 ± 0.09 0.48 ± 0.03 ± 0.08
WZ 0.42 ± 0.07 0.44 ± 0.06√s = 13 TeV
Z+jets 4.44 ± 0.30 ± 1.05 2.64 ± 0.22 ± 0.36
tt 0.65 ± 0.02 ± 0.17 1.70 ± 0.05 ± 0.35
WZ 0.53 ± 0.30 0.38 ± 0.24
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Same sign control regionµµ+ll
(d)
Figure 6.1: The observed m12 distributions (filled circles) and the results of the
maximum likelihood fit are presented for the four control regions using the Run 1
data sets: (a) inverted criteria on impact parameter significance, (b) inverted criteria
on isolation, (c) eµ leading dilepton, (d) same-sign subleading dilepton. The fit results
are shown for the total background (black line) as well as the individual components:
Z+jets decomposed into Z + tb, i.e. Z+heavy-flavor jets (blue line) and the Z+light-
flavor jets (green line), tt (dashed red line), and the combined WZ and ZZ(∗) (dashed
gray line), where the WZ and ZZ contributions are estimated from simulation.
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(d)
Figure 6.2: The observed m12 distributions (filled circles) and the results of the
maximum likelihood fit are presented for the four control regions using the Run 2
data sets: (a) inverted criteria on impact parameter significance, (b) inverted criteria
on isolation, (c) eµ leading dilepton, (d) same-sign subleading dilepton. The fit results
are shown for the total background (black line) as well as the individual components:
Z+jets decomposed into Z + tb, i.e. Z+heavy-flavor jets (blue line) and the Z+light-
flavor jets (green line), tt (dashed red line), and the combined WZ and ZZ(∗) (dashed
gray line), where the WZ and ZZ contributions are estimated from simulation.
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6.3.3 ``+ ee background
The `` + ee reducible background originates mainly from light-flavor jets (f),
converted photons (γ) and heavy-flavor semileptonic decays (q). A control region
enriched in events associated with each of these sources is defined, namely the 3`+X
control region, allowing data-driven classification of reconstructed events into matching
sources. The efficiencies needed to extrapolate the different background sources from
the control region into the signal region are obtained separately for each of the f ,
γ, q background sources, in pT and η bins from simulation. These simulation-based
efficiencies are corrected to the ones measured in data using another control region,
denoted as Z+X. The Z+X control region has a leading lepton pair compatible with
the decay of a Z boson, passing the full event selection. And the additional object
(X) satisfies the relaxed requirements as for the X in the 3`+X control region.
Candidates in the 3` + X control region are selected by following the standard
analysis selections, but requiring relaxed selections on the lowest-ET electron: only a
track with a minimum number of silicon hits which matches a cluster is required. The
electron identification and isolation/impact parameter significance selection criteria
are not applied. For the Run 2 analysis, the vertex and impact parameter significance
requirements are applied to reject the q background source, which is then estimated
from MC simulation. In addition, the subleading electron pair is required to have the
same sign for both charges (SS) to suppress contributions from ZZ(∗) background. A
residual ZZ(∗) component with a magnitude of 5% of the background estimate survives
the SS selection, and is subtracted from the final estimate based on MC simulation.
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The yields of different background sources are extracted from a template fit. For
the Run 1 analysis, two observables are used in the fit: the number of hits in the
innermost layer of the pixel detector (nB-layerhits ) and the ratio of the number of high-
threshold to low-threshold TRT hits (rTRT), allowing separation of the f , γ and q
components, since most photons convert after the innermost pixel layer, and hadrons
faking electrons have a lower rTRT compared to conversions and heavy-flavor electrons.
For the Run 2 analysis, since the q component is removed by applying the impact
parameter significance requirements, only the number of pixel hits (nInnerPix) is used,
defined as the number of IBL hits, or the number of hits on the next-to-innermost pixel
layer when such hits are expected due to a dead area of the IBL. The fitted results
are shown in Figure 6.3 for the Run 1 data sets and in Figure 6.4 for the Run 2 data
sets. The sPlot method [139] is used to unfold the contributions from the different
background sources as a function of electron pT.
To extrapolate the f , γ and q components (the q component is only presented in
the Run 1 analysis) from the 3`+X control region to the signal region, the efficiency
for the different components to satisfy all selection criteria is obtained from the Z+X
simulation, and adjusted to match the measured efficiency in data. The systematic
uncertainty is dominated by the simulation efficiency corrections, corresponding to
30%, 20%, 25% uncertainties for the f , γ, q, respectively, for the Run 1 analysis, and
about 23% uncertainties for the f and γ for the Run 2 analysis. The final results
for treducible backgrounds in the 2µ2e and 4e channels are given in Table 6.3 for the
Higgs analysis and the high-mass analysis.
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Blayer
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(b)
Figure 6.3: The results of a simultaneous fit to (a) nB-layerhits , the number of hits in
the innermost pixel layer, and (b) rTRT, the ratio of the number of high-threshold to
low-threshold TRT hits, for the background sources in the 3`+X control region. The
fit is performed separately for the 2µ2e and 4e channels and summed together in the
present plots. The data are represented by the filled circles. The sources of back-
ground electrons are denoted as light-flavor jets faking an electron (f , green dashed
histogram), photon conversion (γ, blue dashed histogram) and electrons from heavy-
flavor quark semileptonic decays (q, red dashed histogram). The total background is
given by the solid blue histogram.
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InnerPixn
0 1 2 3
Events
1
10
210
310
410
Data
Fit
f
γ
ATLAS Internal
llee, 3L+X CR1
13 TeV, 36.5 fb
(a)
Figure 6.4: The results of a fit to nInnerPix, the number of IBL hits, or the number of
hits on the next-to-innermost pixel layer when such hits are expected due to a dead area
of the IBL, for background sources in the 3`+X control region. The fit is performed
separately for the 2µ2e and 4e channels and summed together in the present plots.
The data are represented by the filled circles. The sources of background electrons are
denoted as light-flavor jets faking an electron (f , green dashed histogram) and photon
conversion (γ, yellow filled histogram). The number of electrons from semileptonic
decays of heavy-flavor quarks are negligibly small. The total background is given by
the solid red histogram.
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Table 6.3: The fit results for the 3` + X control region, the extrapolation factors
and the signal region yields for the reducible `` + ee background. The sources of
background electrons are denoted as light-flavor jets faking an electron (f), photon
conversion (γ) and electrons from heavy-flavor quark semileptonic decays (q). The
second column gives the fit yield of each component in the 3` + X control region.
The corresponding extrapolation efficiency and signal region yield are in the next two
columns. The background values represent the sum of the 2µ2e and 4e channels. The
uncertainties are a combination of the statistical and systematic uncertainties.Type Fit yield in control region Extrapolation factor Yield in signal region√
s = 7 TeV
f 391 ± 29 0.010 ± 0.001 3.9 ± 0.9
γ 19 ± 9 0.10 ± 0.02 2.0 ± 1.0
q 5.1 ± 1.0 0.10 ± 0.03 0.51 ± 0.15√s = 8 TeV
f 894 ± 44 0.0034 ± 0.0004 3.1 ± 1.0
γ 48 ± 15 0.024 ± 0.004 1.1 ± 0.6
q 18.3 ± 3.6 0.10 ± 0.02 1.8 ± 0.5√s = 13 TeV
f 3075 ± 56 0.0020 ± 0.0004 5.68 ± 1.24
γ 208 ± 17 0.0071 ± 0.0014 1.34 ± 0.44
q (MC-based estimation) 6.34 ± 1.93
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6.4 Statistical methodology
The statistical interpretation of an analysis can be summarized by either a p-
value for discovery purposes or an upper limit on one or more parameters of the signal
model under test. The p-value is defined as the probability, under an assumption, of
finding data of equal or greater incompatibility with the predictions of the assumption.
The measure of incompatibility is based on a test statistic, such as the number of
events in the signal region. When the look-elsewhere-else effect [140] is taken into
account in calculating a p-value, the p-value is called global p-value, otherwise it is
called local p-value. An equivalent formulation of p-value in terms of the number
of standard deviation (σ), Z, referred to as the significance, is defined such that a
Gaussian distributed variable found Z standard deviation(s) above its mean has an
upper-tail probability equal to the p-value. That is Z = Φ−1(1 − p), where Φ−1 is
the quantile (inverse of the cumulative distribution) of the standard Gaussian. For
example, a significance of 5 σ (Z = 5) equals to a p-value of 2.866×10−7. The statistical
treatment follows the procedure for the Higgs-boson search combination [141,142], and
is implemented with RooFit [143] and RooStats [144].
Construction of likelihood The test statistic employed for hypothesis testing and
limit setting is the profiled likelihood ratio Λ(µ):
Λ(µ) =L(µ,
ˆθ(α))
L(µ, θ)(6.1)
where the µ are the parameters of interest, θ are the nuisance parameters that repre-
sent systematic uncertainties estimated in auxiliary measurements. The µ and θ refer
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to the unconditional maximum likelihood estimators of µ and θ, respectively, and the
ˆθ(µ) refers to the best fitted values of θ when the parameters of interest are set to µ
as constant values. The Neyman-Pearson lemma [145] indicates that the test statistic
of likelihood offers good separation power for any type of hypotheses.
The final likelihood L is a product of the likelihood for each category Li, each
Li consisting of a Poisson term, likelihood functions and Gaussian constraint terms:
L =c∏i
Li
Li = Poisson(ni|Si(µ,θ) +Bi(θ))
×
[ni∏j=1
S(µ,θ)f iS(xj;θ) +Bif iB(xj;θ)
Si(µ,θ) +Bi(θ)
]·Gauss(θ; 0, 1)
(6.2)
where Si and Bi are the expected number of signal and background events in category
i. fX(x;θ), the probability density function of the observable x, usually depends on
some systematic uncertainties θ, such as lepton energy/momentum scale uncertainties.
The expected number of signal events is parameterized as:
S = µ× σ × BRp × BRd × A× C ×∫L × (1 + ε(θ)) (6.3)
where µ is the signal strength, σ is the total cross section; A×C is the acceptance times
efficiency;∫L is the integrated luminosity of the dataset; BRp is the branching ratio
of H → ZZ(∗) and BRd is that of ZZ(∗) → `+`−`+`−. The advantage of factorizing
the two branching ratios is that for the search for additional scalars, BRp depends on
the nature of the additional scalars but BRd is known from the SM when both ZZ
are on-shell. BRd(ZZ → `+`−`+`−) = 0.00452, where ` stands for a e or µ, allowing
for setting upper limits on σ × BRp. The term ε(θ) represents the relative impact of
systematic uncertainties θ.
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Probability distribution function of the likelihood Because only upwards de-
viation is of physical interests, equation 6.1 is extended to:
qµ =
−2 ln Λ(µ) µ ≤ µ
0 µ > µ
=
−2 ln L(µ,θ)
L(0,ˆθ)
µ < 0,
−2 ln L(µ,θ)
L(µ,ˆθ)
0 ≤ µ < µ,
0 µ > µ.
(6.4)
for setting limits and extended to:
qµ =
−2 ln Λ(µ) µ ≥ µ
0 µ < µ
(6.5)
for calculating p-value.
Based on the results due to Wilks [146] and Wald [147], Ref. [148] finds the
probability distribution function of the profiled likelihood ratio can be approximated
by a χ2 function with the same number of degrees of freedom as the one in the
parameters of the interest. Consequently, the significance of the deviation of data from
background-only expectations can be obtained simply by Zµ = Φ−1(1− pµ) =√qµ.
The limit setting is based on the CLs prescription [149], which protects from
excluding the regions that the analysis is not sensitive to. The confidence level CLs
is defined as CLs = ps+b1−pb
, where ps+b is the p-value of signal plus background Asimov
data 1, and pb is the p-value of background-only Asimov data. In general, the probabil-
ity distribution function of qµ for signal plus background and background-only asimov
data follows the asymptotic assumption [148], but the assumption fails if the number
of expected background events is too small, for example less than one. Therefore, the
1 a single representative data set of the ensemble of simulated data sets.
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probability distribution functions constructed from pseudo experiments are used as a
cross check.
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Chapter 7
The observation of the SM Higgs boson in
the `+`−`+`− final state
7.1 Overview
The search for the SM Higgs boson in the `+`−`+`− final state in ATLAS was first
reported in Ref. [150] in September 2011, using an integrated luminosity of 2.1 fb−1
pp collision data at√s = 7 TeV. The SM Higgs boson was excluded at 95% confidence
level (CL) in the mass ranges 191–197, 199–200 and 214–224 GeV. Five months later
(February 2012), this search was updated in Ref. [151] with an integrated luminosity
of 4.8 fb−1 pp collision data at√s = 7 TeV. The SM Higgs boson was excluded at 95%
CL in the mass ranges 134–156, 182–233 and 256–265 GeV. In the same paper, three
excesses were reported with local significances of 2.1, 2.2 and 2.1 standard deviations
at 125 GeV, 244 GeV and 500 GeV, respectively. Another five months later (July 2012),
ATLAS reported the observation of a new particle in the combined searches for the
SM Higgs boson, where the four-lepton analysis was the most sensitive channel for a
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125 GeV SM Higgs boson with an expected significance of 2.7 standard deviations [12].
Although the SM Higgs boson was discovered by the combination of different decay
channels, it is of great interest to discover the Higgs boson independently in the four-
lepton final state alone. After the discovery of a new particle, the four-lepton analysis
was fully optimized to search for and measure a SM Higgs boson with a mass of
about 125 GeV. Section 7.2 describes the categorization strategies that are designed
to probe different Higgs production modes, thus enhancing the overall sensitivities.
Background estimates are presented in Section 7.3. Since the mass of the Higgs boson
was known [12,152] and other properties could be simulated, the Run 1 Higgs analysis
employed multivariate techniques in most categories to distinguish either signal from
ZZ(∗) background or one production mode from others, as presented in Section 7.4.
Furthermore, this analysis conducted two-dimensional fits in some categories to reduce
the statistical uncertainties. Section 7.5 discusses the signal and background modeling
in each category, followed by the systematic uncertainties in Section 7.6. Final results
based on the LHC Run 1 data sets are then presented in Section 7.7.
7.2 Event categorization
The four-lepton candidates passing the selections described in Chapter 6 are clas-
sified into one of these categories: VBF enriched, VH-hadronic enriched, VH-leptonic
enriched or ggF enriched. A schematic view of the event categorization strategy is
shown in Fig. 7.1.
The VBF enriched category is defined by events with two high-pT jets, which
are required to have pT > 25(30) GeV for |η| < 2.5 (2.5 < |η| < 4.5). If more than
two jets fulfill these requirements, the two highest-pT jets are selected as VBF jets.
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ATLAS
l 4→ ZZ* →H
selectionl4
High mass two jets
VBFVBF enriched
Low mass two jets
jj)H→ jj)H, Z(→W(
Additional lepton
)Hll →)H, Z(νl →W(
VH enriched
ggF ggF enriched
Figure 7.1: Schematic view of the event categorization. Events are required to pass
the four-lepton selections, and then they are classified into one of the four categories
which are checked sequentially: VBF enriched, VH-hadronic enriched, VH-leptonic
enriched, or ggF enriched.
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The event is assigned to the VBF enriched category if the invariant mass of the dijet
system, mjj, is greater than 130 GeV, leading to a signal efficiency of approximately
55%. This category has a considerable contamination from ggF events, with 54% of
the expected events in this category arising from ggF production.
Events that do not satisfy the VBF enriched criteria are considered for the VH-
hadronic enriched category. The same jet-related requirements are applied but with
40 < mjj < 130 GeV. Moreover, the candidate has to fulfill a requirement on the
output weight of a specific multivariate discriminant, presented in Section 7.4. The
signal efficiency for requiring two jets is 48% for VH and applying the multivariate
discriminant brings the overall signal efficiency to 25%.
Events failing to satisfy the above criteria are next considered for the VH-leptonic
enriched category. Events are assigned to this category if there is an extra lepton
(e or µ), in addition to the four-leptons forming the Higgs boson candidate, with
pT > 8 GeV and satisfying the same lepton requirements. The signal efficiency for
the extra vector boson for the VH-leptonic enriched category is around 90% (100%)
for the W (Z), where the Z has two leptons which can pass the extra lepton selection.
Finally, events that are not assigned to any of the above categories are as-
sociated with the ggF enriched category. Table 7.4 shows the expected yields for
Higgs boson production in each category from each of the production mechanism, for
mH = 125 GeV and 4.5 fb−1 at√s = 7 TeV and 20.3 fb−1 at
√s = 8 TeV.
7.3 Background estimation
The methodologies used to estimate the background yields are described in Chap-
ter 6.3. For the reducible backgrounds, the fraction of background in each category
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Table 7.1: The expected number of events in each category (VBF enriched, VH-
hadronic enriched, VH-leptonic enriched, ggF enriched), after all analysis criteria are
applied, for each signal production mechanism (ggF/bbH/ttH, VBF, VH) at mH =
125 GeV, for 4.5 fb−1 at√s = 7 TeV and 20.3 fb−1 at
√s = 8 TeV. The requirement
m4` > 110 GeV is appliedCategory gg → H, qq → bbH/ttH qq′ → Hqq′ qq → V H√
s = 7 TeV
VBF enriched 0.13 ± 0.04 0.137 ± 0.009 0.015 ± 0.001
VH-hadronic enriched 0.053 ± 0.018 0.007 ± 0.001 0.038 ± 0.002
VH-leptonic enriched 0.005 ± 0.001 0.0007 ± 0.0001 0.023 ± 0.002
ggF enriched 2.05 ± 0.25 0.114 ± 0.005 0.067 ± 0.003√s = 8 TeV
VBF enriched 0.13 ± 0.04 0.69 ± 0.05 0.10 ± 0.01
VH-hadronic enriched 1.2 ± 0.4 0.030 ± 0.004 0.21 ± 0.01
VH-leptonic enriched 0.41 ± 0.14 0.0009 ± 0.0002 0.13 ± 0.01
ggF enriched 12.0 ± 1.4 0.52 ± 0.02 0.37 ± 0.02
is evaluated using simulation. Applying these fractions to the background yields of
``+µµ described in Section 6.3.2 and that of ``+ee in Section 6.3.3 gives the reducible
background estimates per category shown in Table 7.2.
7.4 Multivariate techniques
The analysis sensitivity is improved by employing three multivariate discrimi-
nants to distinguish between different classes of four-lepton events: one to separate
the Higgs boson signal from the ZZ(∗) background in the inclusive analysis, and two
to separate the VBF- and VH-produced Higgs boson signal from the ggF-produced
Higgs boson signal in the VBF enriched and VH-hadronic enriched categories. These
discriminants are based on boosted decision trees (BDTs) [153].
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Table 7.2: Summary of the reducible-background estimates for the data recorded at
√s = 7 TeV and
√s = 8 TeV for the full m4` mass range. The quoted uncertainties
include the combined statistical and systematic components.Channel ggF enriched VBF enriched VH-hadronic enriched VH-leptonic enriched√
s = 7 TeV
``+ µµ 0.98 ± 0.32 0.12 ± 0.08 0.04 ± 0.02 0.004 ± 0.004
``+ ee 5.5 ± 1.2 0.51 ± 0.6 0.20 ± 0.16 0.06 ± 0.11√s = 8 TeV
``+ µµ 6.7 ± 1.4 0.6 ± 0.6 0.21 ± 0.13 0.003 ± 0.003
``+ ee 5.1 ± 1.4 0.5 ± 0.6 0.19 ± 0.15 0.06 ± 0.11
BDT for ZZ(∗) background rejection The differences in the kinematics of the
H → ZZ(∗) → `+`−`+`− decay and the ZZ(∗) background are incorporated into
a BDT discriminant (BDTZZ(∗)). The training is done using fully simulated H →
ZZ(∗) → `+`−`+`− signal events, generated with mH = 125 GeV for ggF production
and qq → ZZ(∗) background events. Only events satisfying the inclusive event selection
requirements and with 115 < m4` < 130 GeV are considered. This range contains
95% of the signal and is asymmetric around 125 GeV to include the residual effects
of FSR and bremsstrahlung. The discriminating variables used in the training are
the transverse momentum of the four-lepton system (p4`T ); the pseudorapidity of the
four-lepton system (η4`), correlated to the p4`T ; and a matrix-element-based kinematic
discriminant (DZZ(∗)). The discriminant DZZ(∗) is defined as
DZZ(∗) = ln
(|Msig|2
|MZZ|2
)where Msig corresponds to the matrix element for the signal process, while MZZ is
the matrix element for the ZZ(∗) background process. The matrix elements for both
signal and background are computed at leading order using MadGraph [77]. The
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matrix element for the signal is evaluated according to the SM hypothesis of a scalar
boson with spin-parity JP = 0+ [154] and under the assumption that mH = m4`.
Figures 7.2(a)– 7.2(c) show the distributions of the variables used to train the BDTZZ(∗)
classifier for the signal and the ZZ(∗) background. The separation between a SM Higgs
signal and the ZZ(∗) background can be seen in Fig. 7.2(d).
As discussed in Sec. 7.5, the BDTZZ(∗) output is exploited in the two-dimensional
model built to measure the Higgs boson mass, the inclusive signal strength and the
signal strength in the ggF enriched category. The signal strength µ is defined as the
ratio of the measured Higgs boson production cross section times the branching ratio
over that predicted by the SM. Therefore, by definition, the SM predicted value of
the signal strength for the SM Higgs boson signla is 1 and for the SM background is
0.
BDT for categorization For event categorization, two separate BDT classifier were
developed to discriminate against ggF production: one for VBF production (BDTVBF)
and another for the vector boson hadronic decays of VH production (BDTVH). In the
first case the BDT output is used as an observable together with m4` in a maximum
likelihood fit for the VBF category, while in the latter case the BDT output value
is used as a selection requirement for the event to be classified in the VH-hadronic
enriched category, as discussed in Sec. 7.2. In both cases the same five discriminating
variables are used. In order of decreasing separation power between the two production
modes, the variables are (a) invariant mass of the dijet system, (b) pseudorapidity
separation between the two jets (|∆ηjj|), (c) transverse momentum of each jet, and
(d) pseudorapidity of the leading jet.
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outputZZ*
D
6 4 2 0 2 4 6 8
outp
ut / 0.5
ZZ
*1/N
dN
/dD
0
0.05
0.1
0.15
0.2
0.25ATLAS Simulation
l4→ZZ*→H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
=125 GeV)H
ggF (m
ZZ*
(a)
[GeV]l4
Tp
0 50 100 150 200 250 300 350
/ 1
0 G
eV
l4 T
1/N
dN
/dp
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4ATLAS Simulation
l4→ZZ*→H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
=125 GeV)H
ggF (m
ZZ*
(b)
l4η8 6 4 2 0 2 4 6 8
/ 0
.5l
4 η1/N
dN
/d
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14 ATLAS Simulation
l4→ZZ*→H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
=125 GeV)H
ggF (m
ZZ*
(c)
outputZZ*
BDT
1 0.6 0.2 0.2 0.6 1
outp
ut / 0.0
5Z
Z*
1/N
dN
/dB
DT
0
0.02
0.04
0.06
0.08
0.1
0.12ATLAS Simulation
l4→ZZ*→H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
=125 GeV)H
ggF (m
ZZ*
(d)
Figure 7.2: Distributions for signal (blue) and ZZ(∗) background (red) events, showing
(a) DZZ(∗) output, (b) p4`T and (c) η4` after the inclusive analysis selection in the mass
range 115 < m4` < 130 GeV used for the training of the BDTZZ(∗) classifier. (d)
output distribution for signal (blue) and ZZ(∗) background (red) in the mass range of
115 < m4` < 130 GeV. All histograms are normalized to the same area.
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For the training of the BDT discriminant, fully simulated four-lepton Higgs
boson signal events produced through ggF and VBF production and hadronically de-
caying vector boson events for VH production are used. The distributions of these
variables for BDTVBF are presented in Figs. 7.3(a)– 7.3(e), where all the expected
features of the VBF production of a Higgs boson can be seen: the dijet system has a
high invariant mass and the two jets are emitted in opposite high-|η| regions with a
considerable ∆η separation between them. The jets from ggF production, on the other
hand, are more centrally produced and have a smaller invariant mass and ∆η sepa-
ration. The separation between VBF and ggF can be seen in the output of BDTVBF
in Fig 7.3(f), where the separation between VBF and ZZ(∗) is found to be similar.
The output of BDTVBF is unchanged for various mass points around the main train-
ing mass of mH = 125 GeV. For variables entering the BDTVH discriminant, the
invariant mass of the dijet system, which peaks at the Z mass, exhibits the most im-
portant difference between ggF and VH production modes. The other variables have
less separation power. The corresponding separation for BDTVH is shown in Fig. 7.4.
As described in Sec. 7.2, the VH-hadronic enriched category applies a selection on the
BDTVH discriminant (< −0.4) which optimizes the signal significance.
7.5 Signal and background modeling
To enhance analysis sensitivities different discriminants are used in different
categories. In the ggF-enriched category, a two-dimensional (2D) fit to m4` and
the BDTZZ(∗) output (OBDTZZ(∗)
) is used, because it provides the smallest expected
uncertainties for the inclusive signal strength measurements and the largest expected
significance over a background hypothesis. A kernel density estimation method [155]
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[GeV]jj
m
200 400 600 800 1000
/ 1
0 G
eV
jj1/N
dN
/dm
0
0.02
0.04
0.06
0.08
0.1 Simulation ATLAS
l 4→ ZZ* →H 1
Ldt = 4.5 fb∫ = 7 TeV s1
Ldt = 20.3 fb∫ = 8 TeV s
categoryVBF enriched
=125 GeVH
m
ggF
VBF
(a)
|jj
η∆|
0 1 2 3 4 5 6 7 8
| / 0.2
jjη∆
1/N
dN
/d|
0
0.02
0.04
0.06
0.08
0.1 Simulation ATLAS
l 4→ ZZ* →H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
categoryVBF enriched
=125 GeVH
m
ggF
VBF
(b)
[GeV]T
Leading Jet p
50 100 150 200 250 300 350 400
/ 1
0 G
eV
T1/N
dN
/dp
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Simulation ATLAS
l 4→ ZZ* →H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
categoryVBF enriched
=125 GeVH
m
ggF
VBF
(c)
[GeV]T
Subleading Jet p
50 100 150 200
/ 4
GeV
T1/N
dN
/dp
0
0.05
0.1
0.15
0.2
0.25
Simulation ATLAS
l 4→ ZZ* →H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
categoryVBF enriched
=125 GeVH
m
ggF
VBF
(d)
ηLeading Jet
4 3 2 1 0 1 2 3 4
/ 0
.2η
1/N
dN
/d
0
0.01
0.02
0.03
0.04
0.05
0.06
Simulation ATLAS
l 4→ ZZ* →H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
categoryVBF enriched
=125 GeVH
m
ggF
VBF
(e)
outputVBF
BDT
1 0.6 0.2 0.2 0.6 1 / 0
.05
VB
F1/N
dN
/dB
DT
0
0.02
0.04
0.06
0.08
0.1
0.12Simulation ATLAS
l 4→ ZZ* →H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
categoryVBF enriched
=125 GeVH
m
ggF
VBF
ZZ*
(f)
Figure 7.3: Distributions of kinematic variables for signal (VBF events, green) and
background (ggF events, blue) events used in the training of the BDTVBF: (a) dijet
invariant mass, (b) dijet η separation, (c) leading jet pT, (d) subleading jet pT, (e)
leading jet η, (f) output distributions of BDTVBF for VBF and ggF events as well as
the ZZ(∗) background (red). All histograms are normalized to the same area.
uses fully simulated events to obtain smooth distributions for the 2D signal models.
These distributions are produced using samples events at 15 different mH values in the
range 115–130 GeV and parametried as functions of mH using B-spline interpolation.
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outputVH
BDT
1 0.6 0.2 0.2 0.6 1
/ 0
.05
VH
1/N
dN
/dB
DT
0
0.02
0.04
0.06
0.08
0.1
0.12 Simulation ATLAS
l 4→ ZZ* →H
1Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
categoryVHhadronic enriched
[GeV] < 130jj
40 < m
=125 GeVH
m
ggF
VH
Figure 7.4: BDTVH discriminant output for the VH-hadronic enriched category for
signal (VH events, dark blue) and background (ggF events, blue) events.
The probability density function for the signal in the 2D fit is
P(m4`, OBDTZZ(∗)|mH) = P(m4`|OBDT
ZZ(∗),mH)P(OBDT
ZZ(∗)|mH)
'
(4∑
n=1
P(m4`|mH)θn(OBDTZZ(∗)
)
)P(OBDT
ZZ(∗)|mH)
(7.1)
where θn defines four equal-sized bins for the value of the BDTZZ(∗) output, and Pn rep-
resents the 1D probability density function of the signal in the corresponding BDTZZ(∗)
bin. The variation of the m4` shape is negligible within a signal BDTZZ(∗) bin. The
background model, Pbkg(m4`, OBDTZZ(∗)
), is described using a two-dimensional proba-
bility density. For the ZZ(∗) and reducible `` + µµ backgrounds, the 2D probability
density distributions are derived from simulation, where ``+µµ simulation was shown
to agree well with data in the control region. For the `` + ee background model,
the two dimensional probability density can only be obtained from data, which is
done using the 3`+X data control region weighted with the transfer factor to match
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the kinematics of the signal region. Figure 7.5 shows the probability density in the
OBDTZZ(∗)
–m4` plane, for the signal with mH = 125 GeV, the ZZ(∗) background from
simulation and the reducible background from the data control region. With respect
to a 1D approach, there is an expected reduction of the statistical uncertainty for
the inclusive signal strength measurements, which is estimated from simulation to be
approximately 8% for both measurements. Both the 1D and the 2D models are built
using m4` after applying a Z-mass constraint to m12 during the fit, as described in
Chapter 6. Figure 8.3 shows the m4` distribution for a simulated signal sample with
mH = 125 GeV, after applying the correction for final-state radiation and the Z-mass
constraint for the 4µ, 4e and 2e2µ/2µ2e final states. The width of the reconstructed
Higgs boson mass for mH = 125 GeV ranges between 1.6 GeV (4µ final state) and
2.2 GeV (4e final state) and is expected to be dominated by the experimental resolu-
tion since, for mH of about 125 GeV, the natural width in the SM is approximately
4 MeV.
In the VBF enriched category, where the BDTVBF discriminant is introduced
to separate the ggF-like events from VBF-like events, the 2D probability density
P(m4`, OBDTVBF) is constructed by factorizing the BDTVBF output and m4` distri-
butions. This factorization is justified by the negligible dependence of the BDTVBF
output on m4` for both signal and background. The BDTVBF output dependence on
the Higgs boson mass is negligible and is neglected in the probability density. Adding
the BDTVBF in the VBF enriched category reduces the expected uncertainty on the
signal strength of the VBF and VH production mechanisms µVBF+VH by about 25%.
The improvement in the expected uncertainty on µVBF+VH reaches approximately 35%
after adding the leptonic and hadronic VH categories to the model.
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In the VH-hadronic and VH-leptonic enriched categories, one dimensional
fit to the m4` observable is performed, since for the VH-hadronic enriched category, a
selection on the BDTVH is included in the event selection.
7.6 Systematic uncertainties
The uncertainties on the lepton reconstruction and identification efficiency, and
on the lepton energy or momentum resolution and scale, are determined using samples
of W , Z and J/Ψ decays. The efficiency to trigger, reconstruct and identify electrons
and muons are studied using Z → `` and J/Ψ→ `` decays. The expected impact from
simulation of the associated systematic uncertainties on the signal yield is presented in
Table 7.3. The impact is presented for the individual final states and for all channels
combined.
The level of agreement between data and simulation for the efficiency of the
isolation and impact parameter requirements of the analysis is studied using a tag-
and-probe method. As a result, a small additional uncertainty on the isolation and
impact parameter selection efficiency is applied for electrons with ET below 15 GeV.
The effect of the isolation and impact parameter uncertainties on the signal strength is
given in Table 7.3. The corresponding uncertainty for muons is found to be negligible.
The uncertainties on the data-driven estimates of the background yields are
discussed in Chapter 6.3 and summarized in Table 7.2, and their impact on the signal
strength is given in Table 7.3.
Uncertainties on the predicted Higgs boson pT spectrum due to those on the
PDFs and higher-order corrections are estimated to affect the signal strength by less
than ±1%. The systematic uncertainty of the ZZ(∗) background rate is around ±4%
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[GeV]l4m
outp
ut
ZZ
* B
DT
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1
0.5
0
0.5
1
110 115 120 125 130 135 140
= 1.51)µ = 125 GeV H
(m
Signal
l 4→ ZZ* →H 1
Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
ATLAS Simulation
(a)
[GeV]l4m
outp
ut
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* B
DT
0
0.02
0.04
0.06
0.08
0.1
1
0.5
0
0.5
1
110 115 120 125 130 135 140
Background ZZ*
l 4→ ZZ* →H 1
Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
ATLAS Simulation
(b)
[GeV]l4m
outp
ut
ZZ
* B
DT
0
0.005
0.01
0.015
0.02
0.025
1
0.5
0
0.5
1
110 115 120 125 130 135 140
Z+jets
l 4→ ZZ* →H 1
Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
ATLAS Simulation
(c)
Figure 7.5: Probability density for the signal and different backgrounds normalized
to the expected number of events for the 2011 and 2012 data sets, summing over all
the final states: (a) P(m4`, OBDTZZ(∗)|mH) for the signal assuming mH = 125 GeV, (b)
P(m4`, OBDTZZ(∗)
) for the ZZ(∗) background and (c) P(m4`, OBDTZZ(∗)
) for the reducible
background.
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[GeV]µ4m
80 100 120 140
/ 0
.5 G
eV
µ4
1/N
dN
/dm
0
0.02
0.04
0.06
0.08
0.1
0.12
= 125 GeVHm
Gaussian fit
SimulationATLAS
µ4→ZZ*→H
= 8 TeVs
0.01 GeV±m = 124.92
0.01 GeV± = 1.60 σ
: 17%σ 2±Fraction outside
With Z mass constraint
[GeV]4em
80 100 120 140
/ 0
.5 G
eV
4e
1/N
dN
/dm
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
= 125 GeVHm
Gaussian fit
SimulationATLAS
4e→ZZ*→H
= 8 TeVs
0.02 GeV±m = 124.51
0.02 GeV± = 2.18 σ
: 19%σ 2±Fraction outside
With Z mass constraint
[GeV]µ2e/2e2µ2m
80 100 120 140
/ 0
.5 G
eV
µ2e/2
e2
µ2
1/N
dN
/dm
0
0.02
0.04
0.06
0.08
0.1
= 125 GeVHm
Gaussian fit
SimulationATLAS
µ2e/2e2µ2→ZZ*→H
= 8 TeVs
0.01 GeV±m = 124.78
0.01 GeV± = 1.77 σ
: 20%σ 2±Fraction outside
With Z mass constraint
Figure 7.6: Invariant mass distribution for a simulated signal sample with mH =
125 GeV, superimposed is the Gaussian fit to the m4` peak after the correction for
final-state radiation and the Z-mass constraint.
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for m4` = 125 GeV and increases for higher mass, averaging to around ±6% for the
ZZ(∗) production above 110 GeV.
The main experimental uncertainty relating to categorization strategies is the jet
energy scale determination, including the uncertainties associated with the modeling
of the absolute and relative in situ jet calibrations, as well as the flavor composition
of the jet sample. The impact of the jet uncertainties on the various categories is anti-
correlated because a variation of the jet energy scale results primarily in the migration
of events among the categories. The impact of the jet energy scale uncertainty results
in an uncertainty of about ±10% for the VBF enriched category, ±8% for the VH-
hadronic enriched category, ±1.5% for the VH-leptonic enriched category and ±1.5%
for the ggF enriched category.
7.7 Results
The number of observed candidate events for each of the four decay channels
in a mass window of 120–130 GeV and the signal and background expectations are
presented in Table 7.4. Three events in the mass range 120 < m4` < 130 GeV are
corrected for FSR: one 4µ event and one 2µ2e are corrected for non-collinear FSR,
and one 2µ2e event is corrected for collinear FSR. In the full mass spectrum, there
are 8 (2) events corrected for collinear (noncollinear) FSR, in good agreement with
the expected number of 11 events.
The expected m4` distribution for the backgrounds and the signal hypothesis are
compared with the combined 2011 and 2012 data sets in Figure 7.7. In Figure 7.7,
one observes the single Z → 4` resonance, the threshold of the ZZ production above
180 GeV and a narrow peak around 125 GeV. The Higgs signal is shown for mH =
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Table 7.3: The expected impact of the systematic uncertainties on the signal yield,
derived from simulation, for mH = 125 GeV, are summarized for each of the four final
states for the combined 2011 and 2012 data sets. The symbol “-” signifies that the
systematic uncertainty does not contribute to a particular final state. The last three
systematic uncertainties apply equally to all final states. All uncertainties have been
symmetrized.Source of uncertainty 4µ 2e2µ 2µ2e 4e combined
Electron rec. and id. efficiencies - 1.7% 3.3% 4.4% 1.6%
Electron isolation and IP selection - 0.07% 1.1% 1.2% 0.5%
Electron trigger efficiency - 0.12% 0.05% 0.21% < 0.2%
``+ ee backgrounds - - 3.4% 3.4% 1.3%
Muon rec. and id. efficiencies 1.9% 1.1% 0.8% - 1.5%
Muon trigger efficiency 0.6% 0.03% 0.6% - 0.2%
``+ µµ backgrounds 1.6% 1.6% - - 1.2%
QCD scale uncertainty 6.5%
PDF, αs, uncertainty 6.0%
H → ZZ(∗) branching ratio uncertainty 4.0%
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Table 7.4: The number of events expected and observed for a mH = 125 GeV
hypothesis for the four-lepton final states in a window of 120 < m4` < 130 GeV.
The second column shows the number of expected signal events for the full mass
range, without a selection on m4`. The other columns show for the 120–130 GeV
mass range the number of expected signal events, the number of expected ZZ(∗) and
reducible background events, and the signal-to-background ratio (S/B), together with
the number of observed events for 2011 and 2012 data sets as well as for the combined
sample.Final state Signal full mass range Signal ZZ(∗) Z+jets, tt S/B Expected Observed√
s = 7 TeV
4µ 1.0 ± 0.10 0.91 ± 0.09 0.46 ± 0.02 0.10 ± 0.04 1.7 1.47 ± 0.10 2
2e2µ 0.66 ± 0.06 0.58 ± 0.06 0.32 ± 0.02 0.09 ± 0.03 1.5 0.99 ± 0.07 2
2µ2e 0.50 ± 0.05 0.44 ± 0.04 0.21 ± 0.01 0.36 ± 0.08 0.8 1.01 ± 0.10 1
4e 0.46 ± 0.05 0.39 ± 0.04 0.19 ± 0.01 0.40 ± 0.09 0.7 0.98 ± 0.10 1
Total 2.62 ± 0.26 2.32 ± 0.23 1.17 ± 0.06 0.96 ± 0.18 1.1 4.45 ± 0.30 6√s = 8 TeV
4µ 5.80 ± 0.57 5.28 ± 0.52 2.36 ± 0.12 0.69 ± 0.13 1.7 8.33 ± 0.6 12
2e2µ 3.92 ± 0.39 3.45 ± 0.34 1.67 ± 0.08 0.60 ± 0.10 1.5 5.72 ± 0.37 7
2µ2e 3.06 ± 0.31 2.71 ± 0.28 1.17 ± 0.07 0.36 ± 0.08 1.8 4.23 ± 0.30 5
4e 2.79 ± 0.29 2.38 ± 0.25 1.03 ± 0.07 0.35 ± 0.07 1.7 3.77 ± 0.27 7
Total 15.6 ± 1.6 13.8 ± 1.4 6.24 ± 0.34 2.0 ± 0.28 1.7 22.1 ± 1.5 31√s = 7 TeV and
√s = 8 TeV
4µ 6.80 ± 0.67 6.20 ± 0.61 2.82 ± 0.14 0.79 ± 0.13 1.7 9.81 ± 0.64 14
2e2µ 4.58 ± 0.45 4.04 ± 0.40 1.99 ± 0.10 0.69 ± 0.11 1.5 6.72 ± 0.42 9
2µ2e 3.56 ± 0.36 3.15 ± 0.32 1.38 ± 0.08 0.72 ± 0.12 1.5 5.24 ± 0.35 6
4e 3.25 ± 0.34 2.77 ± 0.29 1.22 ± 0.08 0.76 ± 0.11 1.4 4.75 ± 0.32 8
Total 18.2 ± 1.8 16.2 ± 1.6 7.41 ± 0.40 2.95 ± 0.33 1.6 26.5 ± 1.7 37
125 GeV with a signal strength of 1.51, corresponding to the combined signal strength
(µ) measurement in the H→ ZZ(∗) → `+`−`+`− final state, scaled to this mass by the
expected variation in the SM Higgs boson cross section times branching ratio.
The local p0-value of the observed signal, representing the significance of the
excess relative to the background-only hypothesis, is obtained with the asymptotic
approximation [148] using the 2D fit without any selection on BDTZZ(∗) output and is
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[GeV]l4m
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Events
/ 2
.5 G
eV
0
5
10
15
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35 Data
= 1.51)µ = 125 GeV H
Signal (m
Background ZZ*
tBackground Z+jets, t
Systematic uncertainty
l 4→ ZZ* →H 1
Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
ATLAS
(a)
[GeV]l4m
100 200 300 400 500 600
Events
/ 1
0 G
eV
0
10
20
30
40
50
60
70
80Data
= 1.51)µ = 125 GeV H
Signal (m
Background ZZ*
tBackground Z+jets, t
Systematic uncertainty
l 4→ ZZ* →H 1
Ldt = 4.5 fb∫ = 7 TeV s
1Ldt = 20.3 fb∫ = 8 TeV s
ATLAS
(b)
Figure 7.7: The distribution of the four-lepton invariant mass, m4`, for the selected
candidates (filled circles) compared to the expected signal and background contribu-
tions (filled histograms) for the combined 2011 and 2012 data sets for the mass range
(a) 80–170 GeV, and (b) 80–600 GeV. The signal expectation shown is for a mass
hypothesis of mH = 125 GeV and normalized to µ = 1.51 (see text). The expected
backgrounds are shown separately for the ZZ(∗) (red histogram), and the reducible
Z+jets and tt backgrounds (violet histogram); the systematic uncertainty associated
to the total background contribution is represented by the hatched areas.
shown as a function of mH in Figure 7.8. The local significance of the excess observed
at the measured mass for this channel, 124.51 GeV, is 8.2 standard deviations. At
the value of the Higgs boson mass, mH = 125.36 GeV, obtained from the combination
of the H → ZZ(∗) → `+`−`+`− and H → γγ mass measurement [152], the local
significance decreases to 8.1 standard deviations. The expected significance at these
two masses is 5.8 and 6.2 standard deviations, respectively.
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[GeV]Hm120 122 124 126 128 130
0L
oca
l p
Obs 2012Exp 2012Obs 2011Exp 2011Obs combinationExp combination
ATLAS
l 4→ ZZ*→H1Ldt = 4.5 fb∫=7 TeV s
1Ldt = 20.3 fb∫=8 TeV s
σ2
σ4
σ6
σ81510
1210
910
610
310
1
Figure 7.8: The observed local p0-value for the combination of the 2011 and 2012 data
sets (solid black line) as a function of mH ; the individual results for√s = 7 TeV and
8 TeV are shown separately as red and blue solid lines, respectively. The dashed curves
show the expected median of the local p0-value for the signal hypothesis with a signal
strength µ = 1, when evaluated at the corresponding mH . The horizontal dot-dashed
lines indicate the p0-values corresponding to local significances of 1–8 σ.
The measured Higgs boson mass obtained with the 2D method is mH = 124.51±
0.52 GeV. The signal strength at this value of mH is µ = 1.66+0.398−0.34 (stat)+0.21
−0.14(syst).
The production mechanisms are grouped into the “fermionic” and the “bosonic” ones.
The former consists of ggF, bbH and ttH, while the latter includes the VBF and VH
modes. The measured value for µggF+bbH +ttH is: 1.66+0.45−0.41(stat)+0.25
−0.15(syst); and the
measured value for µVBF+VH is: 0.26+1.60−0.91(stat)+0.36
−0.23(syst).
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Chapter 8
Search for additional heavy scalars in the
`+`−`+`− final states and combination with
results from `+`−νν final states
8.1 Overview
The observation of the SM Higgs boson does not exclude the possibility that
it may be a part of an extended Higgs sector, as predicted by several beyond the
SM models [67, 156]. The search for additional heavy scalars in the `+`−`+`− final
state uses an integrated luminosity of 36.1 fb−1 pp collision data at√s = 13 TeV
collected by ATLAS during 2015 and 2016 to look for a peak structure on top of a
continuous background spectrum in the four-lepton invariant mass distribution. The
signal and background modeling is described in Section 8.2, followed by the evaluation
of systematic uncertainties in Section 8.3. The results in the `+`−`+`− final state are
presented in Section 8.4. In order to improve the sensitivity of searching for a heavy
scalar in the high mass range, results from the `+`−`+`− and `+`−νν final states are
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combined. Section 8.5 briefly introduces the `+`−νν analysis. The relationship of
the systematic uncertainties in the two analyses is important for the combination.
The correlation schemes used to properly correlate the systematic uncertainties in the
two analyses are discussed in Section 8.5.2, followed by the impact of the systematic
uncertainties on the signal cross section in Section 8.5.3. The combined results are
then presented in Section 8.5.4.
8.2 Signal and background modeling
The parameterisation of the reconstructed four-lepton invariant mass m4` distri-
bution for signal and background is based on the MC simulation and used to fit the
data.
In the case of a narrow resonance, the width in m4` is determined by the detector
resolution, which is modelled by the sum of a Crystal Ball (C) function [157,158] and
a Gaussian (G) function:
Ps(m4`) = fC × C(m4`;µ, σC, αC, nC) + (1− fC)× G(m4`;µ, σG).
The Crystal Ball and the Gaussian functions share the same peak value of m4` (µ), but
have different resolution parameters, σC and σG. The αC and nC parameters control the
shape and position of the non-Gaussian tail, and the parameter fC ensures the relative
normalization of the two probability density functions. To improve the stability of the
parameterization in the full mass range considered, the parameter nC is set to a fixed
value. The bias in the extraction of signal yields introduced by using the analytical
function is below 1.5%. The function parameters are determined separately for each
final state using signal simulation, and fitted to first- and second-degree polynomials
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[GeV]l4m
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Fra
ction o
f events
/ 5
GeV
3−10
2−10
1−10
Simulation ATLAS1,fb = 13 TeVs
µ
+µ
e+ + ee+eµ+
µ → ZZ → H
Simulation
Parametrisation
(a)
[GeV]H
m
200 400 600 800 1000 1200 1400
dis
trib
ution [G
eV
]l
4m
RM
S o
f
0
10
20
30
40
50
60
70
Simulation ATLAS1,fb = 13 TeVs
l
+l
l
+l → ZZ → H
µ
+µ
µ
+µ
µ
+µ
e+ + e
e+eµ
+µ
e+e
e+e
(b)
Figure 8.1: (a) Parameterisation of the four-lepton invariant mass (m4`) spectrum
for various resonance mass (mH) hypotheses in the NWA. Markers show the simulated
m4` distribution for three specific values of mH (300, 600, 900 GeV), normalized to
unit area, and the dashed lines show the parameterization used in the 2e2µ channel for
these mass points as well as for intervening ones. (b) RMS of the four-lepton invariant
mass distribution as a function of mH .
in scalar mass mH to interpolate between the generated mass points. The use of
this parameterization for the function parameters introduces an extra bias in the
signal yield and mH extraction of about 1%. An example of this parameterization is
illustrated in Figure 8.1, where the left plot shows the mass distribution for simulated
samples at mH = 300, 600, 900 GeV and the right plot shows the root mean square
(RMS) of the m4` distribution in the range considered for this search.
In the case of the LWA, the particle-level line-shape of m4` is derived from a the-
oretical calculation, as described in Ref. [159], and is then convolved with the detector
resolution, using the same procedure as for the modeling of the narrow resonance.
The m4` distribution for the ZZ continuum background is taken from MC sim-
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ulation, and parameterized by an empirical function for both the quark- and gluon-
initiated processes:
fqqZZ/ggZZ(m4`) = (f1(m4`) + f2(m4`))×H(m0−m4`)×C0 + f3(m4`)×H(m4`−m0),
where:
f1(m4`) = exp(a1 + a2 ·m4`),
f2(m4`) =
{1
2+
1
2erf
(m4` − b1
b2
)}× 1
1 + exp(m4`−b1b3
) ,f3(m4`) = exp
(c1 + c2 ·m4` + c3 ·m2
4` + c4 ·m2.74`
),
C0 =f3(m0)
f1(m0) + f2(m0).
The function’s first part, f1, covers the low-mass part of the spectrum where
one of the Z bosons is off-shell, while f2 models the ZZ threshold around 2·mZ and
f3 describes the high-mass tail. The transition between low- and high-mass parts is
performed by the Heaviside step function H(x) around m0 = 240 GeV. The continuity
of the function around m0 is ensured by the normalization factor C0 that is applied to
the low-mass part. Finally, ai, bi and ci are shape parameters which are obtained by
fitting the m4` distribution in simulation for each category. The uncertainties in the
values of these parameters from the fit are found to be negligible. The MC statistical
uncertainties in the high-mass tail are taken into account by assigning a 1% uncertainty
to c4.
The m4` shapes are extracted from simulation for most background components
(ttV , V V V , `` + µµ and heavy-flavour hadron component of `` + ee), except for the
light-flavour jets and photon conversions in the case of `` + ee background, which is
taken from the control region as described in Section 6.3.3.
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Interference modeling The gluon-initiated production of a heavy scalarH, the SM
h and the gg → ZZ(∗) continuum background all share the same initial and final state,
and thus lead to interference terms in the total amplitude. Theoretical calculations
described in Ref. [160] have shown that the effect of interference could modify the
integrated cross section by up to O(10%), and this effect is enhanced as the width of
the heavy scalar increases. Therefore, a search for a heavy scalar Higgs boson in the
LWA case must properly account for two interference effects: the interference between
the heavy scalar and the SM Higgs boson (denoted by H–h) and between the heavy
scalar and the gg → ZZ(∗) continuum (denoted by H–B).
Assuming that H and h bosons have similar properties, they have the same pro-
duction and decay amplitudes structure and therefore the only difference between the
signal and interference terms in the production cross section comes from the prop-
agator. Hence, the acceptance and resolution of the signal and interference terms
are expected to be the same. The H–h interference is obtained by reweighting the
particle-level line-shape of generated signal events using the following formula:
w(m4`) =2 ·Re
[1
s−sH· 1
(s−sh)∗
]1
|s−sH |2,
where 1/(s− sH(h)
)is the propagator for a scalar (H or h). The particle-level line-
shape is then convolved with the detector resolution function, and the signal and
interference acceptances are assumed to be the same.
In order to extract theH–B interference contribution, signal-only and background-
only samples are subtracted from the generated SBI samples. The extracted particle-
levelm4` distribution for theH–B interference term is then convolved with the detector
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resolution.
Figure 8.2 shows the overlay of the signal, both interference effects and the total
line-shape for different mass and width hypotheses assuming the couplings expected
in the SM for a heavy Higgs boson. As can be seen, the two interference effects tend
to cancel out, and the total interference yield is for the most part positive, enhancing
the signal.
8.3 Systematic Uncertainties
The systematic uncertainties are classified into experimental and theoretical un-
certainties. The first category relates to the reconstruction and identification of the
physics objects (leptons and jets), their energy scale and resolution, and the inte-
grated luminosity. Systematic uncertainties on the data-driven background estimates
are also included in this category. The second category includes uncertainties on the
theoretical description of the signal and background processes.
In both cases the uncertainties are implemented as additional nuisance param-
eters (NP) that are constrained by a Gaussian distribution in the profiled likelihood.
The uncertainties affect the signal acceptance, its selection efficiency and the discrim-
inant distributions as well as the background estimates. Each source of uncertainties
is either fully correlated or anti-correlated among different categories.
Experimental uncertainties The uncertainty on the combined 2015 and 2016 in-
tegrated luminosity is 4.5%. This is derived from a preliminary calibration of the
luminosity scale using x-y beam separation scans performed in May 2016, following a
methodology similar to that detailed in Ref [82].
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385 390 395 400 405 410 415
0.001−
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0.001
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mH
m×=1%H
Γ
340 360 380 400 420 440 460
0.001−
0
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0.005 =400 GeVH
mH
m×=5%H
Γ
250 300 350 400 450 500 550
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0
0.001
0.002
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0.007=400 GeV
Hm
Hm×=10%
HΓ
570 580 590 600 610 620 6300.002−
0
0.002
0.004
0.006
0.008 =600 GeVH
mH
m×=1%H
Γ
500 550 600 650 700
0.001−
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
=600 GeVH
mH
m×=5%H
Γ
450 500 550 600 650 700 750
0.001−
0
0.001
0.002
0.003
0.004
0.005 =600 GeVH
mH
m×=10%H
Γ
770 780 790 800 810 820 830
0.001−
0
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0.002
0.003
0.004
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0.007 =800 GeVH
mH
m×=1%H
Γ
650 700 750 800 850 900 950
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0
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0.007=800 GeV
Hm
Hm×=5%
HΓ
600 700 800 900 1000
0.001−
0
0.001
0.002
0.003
0.004
0.005
0.006
=800 GeVH
mH
m×=10%H
Γ
= 13 TeVs Simulation ATLAS
[GeV]l4
mParticlelevel
]1
[G
eV
l4
m d
N/d
⋅1
/N
Signal + Interference Signal only
InterferenceHh InterferenceHB
Figure 8.2: Particle-level four-lepton mass m4` model for signal only (red), H–h inter-
ference (green), H–B interference (blue) and the sum of the three processes (black).
Three values of the resonance mass mH (400, 600, 800 GeV) are chosen, as well as
three values of the resonance width ΓH (1%, 5%, 10% of mH). The signal cross section,
which determines the relative contribution of the signal and interference, is taken to
be the cross section of the expected limit for each combination of mH and ΓH . The
full model (black) is finally normalised to unity and the other contributions are scaled
accordingly.
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The efficiency of electron selections are broken down to different sources: trigger,
identification, reconstruction and isolation, and derived from data with large statistics
of the J/ψ → `` and Z → `` events. The uncertainties on the reconstruction perfor-
mance are computed by following the method described in Ref [161] for the muons
and Ref [162] for the electrons. Typical uncertainties on the identification efficiencies
ranges from 0.5% to 1.0% for muons and 1.0% to 1.3% for electrons. The uncertainties
on the electron energy scale, muon momentum and their resolutions are small.
The uncertainties on the jet energy scale and resolution have several sources,
including uncertainties on the absolute and relative in situ calibration, the correction
for pile-up, the flavor composition and response. These uncertainties are separated
into independent components, and vary from 6% for jets with transverse momentum
pT = 20 GeV, decreasing to 1% for jets with pT = 200 − 1800 GeV and increasing
again to 3% for jets with higher pT, for the average pile-up conditions of 2015 and
2016 data taking period.
The efficiencies for the lepton triggers in events with reconstructed leptons are
nearly 100%, and hence the related uncertainties are negligible.
Theoretical uncertainties For simulated signal and backgrounds, theoretical mod-
eling uncertainties associated with PDF, missing QCD higher order corrections (via
variations of factorization and renormalization scales), and parton showering uncer-
tainties are considered.
For various signal hypothesis, the dominant theoretical modeling uncertainties
are due to the missing QCD higher order corrections and to the parton showering. The
missing QCD higher order corrections for the events from the ggF production that fall
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into the VBF-enriched category are evaluated using MadGraph5 aMC@NLO and
affect the signal acceptance by 10%. Parton showering uncertainties are of order 10%
and are evaluated by comparing Pythia 8.2 to the HERWIG7 [163] generator.
For the qq → ZZ(∗) background, the effect of the PDF uncertainties in the full
mass range varies between 2% and 5% in all categories, and that of missing QCD
higher order corrections is about 10% in the ggF-enriched categories and 30% in the
VBF-enriched category. The parton showering uncertainties result in less than 1%
impact in the ggF-enriched categories and about 10% impact in the VBF-enriched
category.
For the gg → ZZ(∗) background, as described in Chapter 4, a 60% relative
uncertainty on the inclusive cross section is considered, while a 100% uncertainty is
assigned in the VBF-enriched category.
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8.4 Results and Statistical interpretation
8.4.1 Observed events in signal region
The expected number of events from each SM background within each category,
as well as the observed number of events, are recorded in Table 8.1. The yield in
the mass range m4` > 130 GeV is 1189 events observed in data compared to 1030.5
± 127.8 (including statistical and systematic uncertainty) events for the expected
backgrounds. This corresponds to a 1.2 σ global excess in data. The excess in the
VBF-like category is with a global significance of about 1.3 σ.
Table 8.1: Number of expected and observed events for m4` > 130 GeV, together
with their statistical and systematic uncertainties, for the ggF- and VBF-enriched
categories.
ProcessggF-enriched categories
VBF-enriched category4µ channel 2e2µ channel 4e channel
ZZ 297 ± 1 ± 40 480 ± 1 ± 60 193 ± 1 ± 25 15 ± 0.1 ± 6.0
ZZ (EW) 1.92 ± 0.11 ± 0.19 3.36 ± 0.14 ± 0.33 1.88 ± 0.12 ± 0.20 3.0 ± 0.1 ± 2.2
Z + jets/tt/WZ 3.7 ± 0.1 ± 0.8 7.8 ± 0.1 ± 1.1 4.4 ± 0.1 ± 0.8 0.37 ± 0.01 ± 0.05
Other backgrounds 5.1 ± 0.1 ± 0.6 8.7 ± 0.1 ± 1.0 4.0 ± 0.1 ± 0.5 0.80 ± 0.02 ± 0.30
Total background 308 ± 1 ± 40 500 ± 1 ± 60 203 ± 1 ± 25 19.5 ± 0.2 ± 8.0
Observed 357 545 256 31
Figure 8.3 shows the four-lepton invariant mass (m4`) distribution of the se-
lected candidates compared to the background expectation in the VBF-enriched and
combined ggF-enriched categories. The m4` distribution in ggF-enriched category are
then separated into 4e, 2µ2e and 4µ channels, as shown in Figure 8.4. No events are
observed beyond the plotted range (to 1200 GeV). The excess at around 240 GeV is
observed mostly in the 4e channel, while the one at 700 GeV is observed in all channels
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and categories. In the m4` range [240, 245] GeV, the yield is 45 events observed in
data compared to 28.3 ± 6.3 events for the expected backgrounds; while in the m4`
range [650, 750] GeV, the yield is 16 events observed in data compared to 6.6 ± 2.7
events for the expected backgrounds. The significance of the two excesses evaluated
from maximum likelihood is presented in Section 8.4.2.
Eve
nts
/ 2
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eV
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410
510 ATLAS1 = 13 TeV, 36.1 fbs
l
+l
l
+l → ZZ → H
ggFenriched
Data
ZZ
VVV, +Vtt
tt+jets, Z
(EW)ZZ
Uncertainty
=600 GeV)Hm(NWA signal
obs. limit×5
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1 = 13 TeV, 36.1 fbs
l+
l
l+
l → ZZ → H
VBFenriched
Data
ZZ
(EW)ZZ
VVV, +Vtt
tt+jets, Z
Uncertainty
=600 GeV)Hm(NWA signal
obs. limit×5
[GeV]l4m
200 400 600 800 1000 1200
Pre
dic
tion
Data
0
1
2
3
Figure 8.3: Distribution of the four-lepton invariant mass m4` in the `+`−`+`− final
state for (a) the ggF-enriched category (b) the VBF-enriched category. The last bin
includes the overflow. The simulated mH = 600 GeV signal is normalized to a cross
section corresponding to five times the observed limit given in Section 8.5.4. The
error bars on the data points indicate the statistical uncertainty, while the systematic
uncertainty in the prediction is shown by the hatched band. The lower panels show
the ratio of data to the prediction.
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Events
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1 = 13 TeV, 36.1 fbse+ee+ e→ ZZ → H
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Data
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VVV, +Vtt
tt+jets, Z
(EW)ZZ
Uncertainty
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vents
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Data
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(EW)ZZ
Uncertainty
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µ
+µ
e+ + e
e+eµ
+µ → ZZ → H
ggFenriched
Data
ZZ
VVV, +Vtt
tt+jets, Z
(EW)ZZ
Uncertainty
[GeV]l4m
200 400 600 800 1000 1200
Pre
dic
tion
Data
0.5
1
1.5
(c)
Figure 8.4: Distribution of the four-lepton invariant mass m4` in the `+`−`+`− final
state for (a) the ggF-like 4e category, (b) ggF-like 4µ category and (c) ggF-like 2µ2e
categories category. The error bars on the data points indicate the statistical uncer-
tainty, while the systematic uncertainty in the prediction is shown by the hatched
band. The lower panels show the ratio of data to the prediction.
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8.4.2 p0
Figure 8.5 shows the local p0 as a function of mH for a scalar from gluon-
fusion production under the NWA. Two excesses are observed for m4` around 240
and 700 GeV, each with a local significance of 3.6 σ estimated under the asymptotic
approximation, assuming the signal comes only from the ggF production. The local
p0 has non-trival dependence on the signal hypothesis. It is checked that in the case
of signal models with the LWA, the local significance is lower than the one under the
NWA, indicating the two excesses are with narrow widths. The global significance,
taking into account the look-elsewhere-else effect, is evaluated from pseudo-data in
the range of 200 GeV < mH < 1200 GeV assuming the signal comes only from the
ggF production. Each pseudo-data is generated from the background-only model by
randomizing the global observables and the expected yields, and then it is performed
in the same way as for data to find the largest local significance for each pseudo-data.
Figure 8.6 shows the distribution of the maximum local significance of each pseudo-
experiment. Therefore given the search region it is expected to have a local excess
with a significance of about 2.4 σ. Finally, the global significance of observing an
excess with a local significance of 3.6 σ in the whole searching region is 2.2 σ.
8.4.3 Upper limits
Narrow Width Approximation Limits on the ggF and VBF cross-sections times
branching ratio assuming the Narrow Width Approximation are obtained as a function
of mH with the CLs procedure in the asymptotic approximation. Figure 8.7 presents
the expected and observed limits, at 95% confidence level, on the cross section time
branching ratio of the heavy Higgs decaying to `+`−`+`− final state in steps of com-
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[GeV]S
m
200 300 400 500 600 700 800 900 1000 1100 1200
0Local p
5−10
4−10
3−10
2−10
1−10
1
σ1
σ2
σ3
σ4
Totalµ4
4eµ2e+2e2µ2
VBF
InternalATLAS113 TeV, 36.1 fb
NWA
Figure 8.5: Local p0 derived for a narrow resonance and assuming the signal comes
only from the ggF production, as a function of the resonance mass mH , using the
exclusive ggF-like categories, VBF-like categories and the combined categories. Also
shown are local (dot-dashed line) significance levels.
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h_sigma_s1
Entries 17930
Mean 2.43
Std Dev 0.4626
local significance
1 1.5 2 2.5 3 3.5 4 4.5 50
100
200
300
400
500
600
700most significant excess
Entries 17930
Mean 2.43
Std Dev 0.4626
Figure 8.6: Probability distribution function of the maximum local significance in the
full search range 200 < m4` < 1200 GeV, resulting from each of generated background-
only pseudo-experiments. The mean value stands for the expected local significance
resulting from background fluctuation in the full search range.
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parable to the detector resolution. Without a specfic model, the ratio of the ggF cross
section to the VBF cross section is unknown, therefore, when setting limits on the ggF
production the VBF cross section is profiled, and vice versa. This result is valid for
models in which the width is less than 0.5% of mH .
[GeV]Hm
200 400 600 800 1000 1200
ZZ
) [p
b]
→ B
R(H
×H
) →
(gg
σ9
5%
C.L
. lim
it o
n
4−10
3−10
2−10
1−10 limitsCLObserved
limitsCLExpected
σ 1 ±Expected
σ 2 ±Expected
PreliminaryATLAS113 TeV, 36.1 fb
4l→ZZ→H→gg
ggF
[GeV]Hm
200 400 600 800 1000 1200
ZZ
) [p
b]
→ B
R(H
×H
) →
(qq
σ9
5%
C.L
. lim
it o
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3−10
2−10
1−10
limitsCLObserved
limitsCLExpected
σ 1 ±Expected
σ 2 ±Expected
PreliminaryATLAS113 TeV, 36.1 fb
4l→ZZ→H→qq
VBF
Figure 8.7: The upper limits at 95% confidence level on then σggF×BR(S → ZZ → 4`)
(left) and σV BF ×BR(S → ZZ → 4`) (right) under the NWA.
Large Widths Assumption In the case of signal models under the LWA, limits on
the cross section for the ggF production mode times branching ratio (σggF×BR(H →
ZZ)) are set for three benchmark widths of a heavy scalar. The interference between
the heavy scalar and the SM Higgs boson, H–h, as well as the heavy scalar and the
gg → ZZ(∗) continuum, H–B, are modeled by analytical functions as explained in
Section 8.2. The total signal yields are parameterized as:
S = µ× SH-only +√µ× (IH−B + IH−h)
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where µ is the signal strength modifier, SH-only is the expected number of events
for heavy scalar signal only, and IH−B and IH−h are the yields of the corresponding
interference terms. Figure 8.15 shows the limits for widths of 1%, 5% and 10% of mH ,
respectively. The limits are set for masses of mH higher than 400 GeV.
8.4.4 2HDM interpretation
A search in the context of a CP-conserving 2HDM, described in Section 2.4,
is also presented. Figure 8.9 shows the exclusion limits in the cos(β − α) versus
tan β plane for Type-I and Type-II 2HDMs, for a heavy Higgs boson with a mass of
200 GeV. This mass value is chosen so that the assumption of a narrow-width Higgs
boson is valid over most of the parameter space, and the experimental sensitivity is
maximal. The range of cos(β − α) and tan β presented is limited to the region where
both the assumption of a heavy narrow-width Higgs boson and the purtabativity in
calculating the cross section are valid. The upper limits at a given value of cos(β−α)
and tan β are re-calculated by using the predicted ratio of ggF production rate over
VBF. Figure 8.10 shows the exclusion limits in the cos(β − α) versus mH plane for
cos(β − α) = −0.1. The valid range of cos(β − α) is constrained by the measurement
of the coupling of the SM Higgs boson with the Z-boson (κh), which is proportional
to sin(β − α). From the combined measurement of Higgs couplings at LHC [164], the
measured κh is consistent with the SM prediction within the uncertainty of about 7%,
therefore the chosen cos(β − α) is valid.
The hatched red area in this exclusion plots is the excluded parameter space.
Compared with the results presented in Run 1 [20], the exclusion limits presented here
is almost twice more stringent.
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[GeV]S
m
400 500 600 700 800 900 1000
4l) [fb
]→
ZZ
→
BR
(S×
gg
Fσ
95%
CL lim
its o
n
1−10
1
10 limitsCLObserved
limitsCLExpected
σ 1 ±Expected
σ 2 ±Expected
PreliminaryATLAS113 TeV, 36.5 fb
LWA 1%
(a)
[GeV]S
m
400 500 600 700 800 900 1000
4l) [fb
]→
ZZ
→
BR
(S×
gg
Fσ
95%
CL lim
its o
n
1−10
1
10 limitsCLObserved
limitsCLExpected
σ 1 ±Expected
σ 2 ±Expected
PreliminaryATLAS113 TeV, 36.5 fb
LWA 5%
(b)
[GeV]S
m
400 500 600 700 800 900 1000
4l) [fb
]→
ZZ
→
BR
(S×
gg
Fσ
95%
CL lim
its o
n
1−10
1
10 limitsCLObserved
limitsCLExpected
σ 1 ±Expected
σ 2 ±Expected
PreliminaryATLAS113 TeV, 36.5 fb
LWA 10%
(c)
Figure 8.8: 95% confidence level limits on cross section for ggF production mode times
the branching ratio (σggF ×BR(H → ZZ → 4`)) as function of mH for an additional
heavy scalar assuming a width of 1% (a), 5% (b) and 10% (c) of mH . The green and
yellow bands represent the ±1σ and ±2σ uncertainties on the expected limits.
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)α-βcos(
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=200 GeVHZZ m→H2HDM Type I
Obs 95% CL bandσ1±Exp 95% CL bandσ2±Excluded
)α-βcos(
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ATLASInternal
= 13 TeVs-136.1 fb
=200 GeVHZZ m→H2HDM Type II
Obs 95% CL bandσ1±Exp 95% CL bandσ2±Excluded
)α-βcos(
0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8
βta
n
1−10
1
10
Figure 8.9: The exclusion contour in the plane of tan β and cos(β − α) for mH =
200 GeV for Type-I and Type-II. The green and yellow bands represent the ±1σ
and ±2σ uncertainties on the expected limits. The hatched area shows the observed
exclusion.
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n
1−10
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(b)
Figure 8.10: The exclusion limits as a function of tan β and mH with cos(β−α) = −0.1
for Type-I (a) and Type-II (b) 2HDM. The green and yellow bands represent the ±1σ
and ±2σ uncertainties on the expected limits. The hatched area shows the observed
exclusion.
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8.5 Combination of the results from `+`−`+`− and `+`−νν
The `+`−`+`− final state features excellent mass resolution while the `+`−νν
benefits from a larger branching ratio. The `+`−`+`− and `+`−νν analyses compliment
each other when they are combined, leading to better search sensitivities over the whole
mass range. Section 8.5.1 provides an overview of the search for heavy resonances in
the `+`−νν final state. Section 8.5.2 describes the correlation schemes used in the
combination, Section 8.5.3 discusses the impact of the uncertainties on the signal
cross section and Section 8.5.4 shows the combined results.
8.5.1 Search for heavy resonances in the `+`−νν final state
The search for heavy resonances in the `+`−νν final state selects the events that
contain two oppositely charged isolated leptons originating from an on-shell Z boson
along with a large missing transverse momentum (EmissT ). Different assumptions of
the origin of EmissT lead to different signal models, therefore the `+`−νν final state is
sensitive to different signal models. For example, it is sensitive to the Higgs boson
decays to invisible particles when EmissT is assumed to come from the invisible decay
of the Higgs boson, and sensitive to the dark matter production rate when EmissT is
assumed to come from dark particles that form dark matter. The two results are
reported in Ref. [165], using 36.1 fb−1 pp collision data at√s = 13 TeV collected by
ATLAS. However, in this thesis, EmissT is presumably from the neutrinos that have
decayed from the Z boson. For two on-shell Z bosons, the branching ratio of ZZ →
`+`−νν is 4.044% and that of ZZ → `+`−`+`− is 0.452%, where ` stands for e or µ.
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This search looks for an excess in the transverse mass spectrum mT, defined as:
mT ≡
√[√m2
Z +(p``T)2
+
√m2
Z + (EmissT )
2
]2
−∣∣∣ ~pT
`` + ~EmissT
∣∣∣2 (8.1)
where mZ is the pole mass of the Z boson, p``T is the transverse momentum of the
lepton pair, ~EmissT is the missing transverse momentum and Emiss
T is the magnitude of
~EmissT .
Event Selections The event selections are designed to discriminate against the Z
+ jets, WZ and top-quark backgrounds. Events are required to pass either a single
electron or muon trigger, where different pT thresholds are used depending on the
instantaneous luminosity of the LHC. The trigger efficiency for signal events passing
the final selection is about 99%. Selected events must have exactly two opposite-charge
leptons of the same flavor and “medium” identification, with the more energetic lepton
having pT > 30 GeV and the other one having pT > 20 GeV. The same impact
parameter significance criteria as defined in Chapter 6 are applied to the selected
leptons. Track- and calorimeter-based isolation criteria as defined in Chapter 6 are
also applied to the leptons, but in this analysis the criteria are optimized by adjusting
the isolation threshold so that the selection efficiency of the isolation criteria is 99%
for signal leptons. If an additional lepton with pT > 7 GeV and “loose” identification
is found then the event is rejected, to reduce the amount of the WZ background. In
order to select leptons originating from the decay of a Z boson, the invariant mass
of the lepton pair is required to be in the range of 76 to 106 GeV. Moreover, since a
Z boson originating from the decay of a high-mass particle will be boosted, the two
leptons are required to be produced with a small angular separation ∆R`` < 1.8.
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Events with neutrinos in the final state are selected by imposingEmissT > 120 GeV,
and this requirement heavily reduces the amount of Z + jets background. In signal
events with no initial- or final-state radiation the Z boson is expected to be produced
back-to-back with respect to the missing transverse momentum, and this characteristic
is used to further suppress the Z + jets background. The azimuthal angle between the
dilepton system and the missing transverse momentum (∆Φ(``, ~EmissT )) is thus required
to be greater than 2.7 and the fractional pT difference, defined as |pmiss,jetT − p``T |/p``T ,
to be less than 20%, where pmiss,jetT = | ~Emiss
T +∑
jet ~pTjet|.
Additional selection criteria are applied to keep only events with EmissT originating
from neutrinos rather than detector inefficiencies, poorly reconstructed high-pT muons
or mis-measurements in the hadronic calorimeter. If at least one reconstructed jet has
a pT greater than 100 GeV, the azimuthal angle between the highest-pT jet and the
missing transverse momentum is required to be greater than 0.4. Similarly, if EmissT
is found to be less than 40% of the scalar sum of the transverse momenta of leptons
and jets in the event (HT ), the event is rejected. Finally, to reduce the tt background,
events are rejected whenever a b-jet is found.
The sensitivity of the analysis to the VBF production mode is increased by
creating a dedicated category of VBF-enriched events. An optimization procedure
based on the significance obtained by using signal and background MC samples is
performed and the selection criteria require the presence of at least two jets with pT >
30 GeV checking that the two highest-pT jets are widely separated in η, |∆ηjj| > 4.4,
and have a invariant mass mjj greater than 500 GeV.
The signal acceptance, defined as the ratio of the number of reconstructed events
passing the analysis requirements to the number of simulated events in each category,
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for the `+`−νν analysis is shown in Table 8.2, for the ggF and VBF production modes
as well as for different resonance masses.
Table 8.2: Signal acceptance for the `+`−νν analysis, for both the ggF and VBF
production modes and resonance masses of 300 and 600 GeV. The acceptance is defined
as the ratio of the number of reconstructed events after all selection requirements to
the number of simulated events for each channel/category.
Mass Production modeggF-enriched categories
VBF-enriched categoryµ+µ− channel e+e− channel
300 GeVggF 6% 5% < 0.05%
VBF 2.6% 2.4% 0.7%
600 GeVggF 44% 44% 1%
VBF 27% 27% 13%
The `+`−νν search starts only from 300 GeV because this is where it begins
to improve the combined sensitivity as the acceptance increases due to a kinematic
threshold coming from the EmissT selection criteria, also seen from Table 8.2.
Background Estimation The dominant and irreducible background for this search
is the non-resonant ZZ production which accounts for about 60% of the expected
background events. The second largest background comes from the WZ production
(∼30%) followed by Z + jets production with poorly measured jets (∼6%). Other
sources of background are the WW , tt, Wt and Z → ττ processes (∼3%). Finally,
a small contribution comes from W + jets, single-top quark and multi-jet processes,
with at least one jet mis-identified as an electron or muon, as well as from ttV/V V V
events.
The ZZ production is modeled with MC simulation and normalized to SM pre-
dictions, as explained in Section 4.2. The remaining backgrounds are mostly estimated
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by extrapolating the events in a control region to the signal region using dedicated
transfer factors.
The WZ background is modeled by MC simulation and a correction factor for
its normalization is extracted as the ratio of data events to the simulated events in
a WZ-enriched control region, after subtracting from data the non-WZ background
contribution. The WZ-enriched control region, called the 3` control region, is built
by selecting Z → `` candidates with an additional electron or muon. This additional
lepton is required to pass all selection criteria used for the other two leptons, with the
only difference that its transverse momentum is required to be greater than 7 GeV. The
contamination from Z + jets and tt events is reduced by vetoing events with at least
one reconstructed b-jet and by requiring the transverse mass of W boson (mWT ), built
using the additional lepton and the ~EmissT , to be greater than 60 GeV. The distribution
of the missing transverse momentum for data and simulated events in the 3` control
region is shown in Figure 8.11(a). The correction factor derived in the 3` control region
is found to be 1.29 ± 0.09, where the uncertainty includes effects from the statistics
of the control region as well as from experimental systematic uncertainties. Due to
poor statistics when applying all the VBF selection requirements to the WZ enriched
control sample, the estimate for the VBF-enriched category is performed by including
in the 3` control region only the requirement of at least two jets with pT > 30 GeV.
Finally, a transfer factor is derived from MC simulation by calculating the probability
of events passing all analysis selections and containing two jets with pT > 30 GeV to
satisfy the VBF selections
The non-resonant background includes mainly WW , tt and Wt processes, but
also Z → ττ events in which the τ leptons produce light leptons and EmissT . It is
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estimated by using a control sample of events with lepton pairs of different flavour
(e±µ∓), passing all analysis selection criteria. Figure 8.11(b) shows the missing trans-
verse momentum distribution for e±µ∓ events in data and simulation after applying
the dilepton invariant mass selection but before applying the other selection require-
ments. The non-resonant background in the e+e− and µ+µ− channels is estimated by
applying a scale factor (f) to the events in the e±µ∓ control region, such that:
Nbkgee =
1
2×Ndata,sub
eµ × f, Nbkgµµ =
1
2×Ndata,sub
eµ × 1
f, (8.2)
where Nbkgee and Nbkg
µµ are the numbers of electron and muon pair events estimated
in the signal region and Ndata,subeµ is the number of events in the e±µ∓ control sample
with ZZ, WZ and other small backgrounds subtracted using simulation. The factor f
takes into account the different selection efficiency of e+e− and µ+µ− pairs at the level
of the Z → `` selection, and is measured from data as f 2 = Ndataee /Ndata
µµ , where Ndataee
and Ndataµµ are the number of events passing the Z boson mass requirement (76 < m`` <
106 GeV) in the electron and muon channel respectively. As no events survive in the
e±µ∓ control region after applying the full VBF selections, the background estimate
is performed by including only the requirement of at least two jets with pT > 30 GeV.
The efficiency of the remaining selection criteria on ∆ηjj and mjj is obtained from
simulated events.
The number of Z + jets background events in the signal region is estimated from
data, using a so-called ABCD method [166], since events with no genuine EmissT in the
final state are difficult to model using simulation. The method combines the selection
requirements presented in Section 8.5.1 (with nb−jets representing the number of b-jets
in the event) into two Boolean discriminants, V1 and V2, defined as:
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210
310
410
510
610 PreliminaryATLAS1 = 13 TeV, 36.1 fbs
νν
l+
l → ZZ → H
Control Regionl3
Data
WZ
ZZ
+jetsZ
ττ→Z, tt, Wt, WW
Other backgrounds
Uncertainty
[GeV]missTE
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210
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410
510
610
710
810 PreliminaryATLAS1 = 13 TeV, 36.1 fbs
νν
l+
l → ZZ → H
Control Regionµe
Data
ττ→Z, tt, Wt, WW
+jetsZ
WZ
Other backgrounds
ZZ
Uncertainty
[GeV]missTE
0 100 200 300 400 500 600
Pre
dic
tion
Data
0.5
1
1.5
(b)
Figure 8.11: Missing transverse momentum distribution (a) for events in the 3` control
region as defined in the text and (b) for e±µ∓ lepton pairs after applying the dilepton
invariant mass selection. The backgrounds are determined following the description in
Section 8.5.1 and the last bin includes the overflow. The error bars on the data points
indicate the statistical uncertainty, while the systematic uncertainty on the prediction
is shown by the hatched band. The bottom part of the figures shows the ratio of data
over expectation.
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V1 ≡ EmissT > 120 GeV and Emiss
T /HT > 0.4, (8.3)
V2 ≡ |pmiss,jetT − p``T |/p``T < 0.2 and ∆φ(``, ~Emiss
T ) > 2.7 and ∆R`` < 1.8 and nb−jets = 0,
(8.4)
with all events required to pass the trigger and dilepton invariant mass selections.
The signal region (A) is thus obtained by requiring both V1 and V2 to be true, control
regions B and C require only one of the two booleans to be false (V1 and V2 respec-
tively) and finally control region D is defined by requesting both V1 and V2 to be
false. With this definition, an estimate of the number of events in region A is given by
N estA = Nobs
C × (NobsB /Nobs
D ), where NobsX is the number of events observed in region X
after subtracting non-Z-boson backgrounds. This relation holds as long as the corre-
lation between V1 and V2 is small, and this is obtained by introducing two additional
requirements on control regions B and D, namely EmissT > 30 GeV and Emiss
T /HT > 0.1.
The estimation of the Z + jets background was cross-checked with another approach
in which a control region is defined by inverting the analysis selection on EmissT /HT
and then using Z + jets Monte Carlo simulation to perform the extrapolation to the
signal region, yielding results compatible with the ABCD method. Finally, the esti-
mate for the VBF-enriched category is performed by extrapolating the inclusive result
obtained with the ABCD method to the VBF signal region, extracting the efficiency
of the two-jet, ∆ηjj and mjj selection criteria from Z + jets simulation.
The W + jets and multi-jet backgrounds are estimated from data using a so-
called fake factor method [167]. A control region enriched in fake leptons is designed by
requiring one lepton to pass all analysis requirements (baseline selection) and the other
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one to fail either the lepton “medium” identification or the isolation criteria (inverted
selection). The background in the signal region is then derived using a transfer factor,
measured in a data sample enriched in Z + jets events, as the ratio of jets passing the
baseline selection to those passing the inverted selection.
Finally, the background from the ttV and V V V processes is estimated using MC
simulation.
Signal and background modelling The modeling of the transverse invariant mass
mT distribution for signal and background is based on the templates derived from fully
simulated events and afterwards used to fit the data. In the case of a narrow width
resonance, simulated MC events generated at fixed mass hypotheses as described in
Section 4.2 are used as the inputs in the moment morphing technique [168] to obtain
the mT distribution for any other mass hypothesis.
The extraction of the interference terms for the LWA case is performed in the
same way as in the `+`−`+`− final state, as described in Section 8.2. In the case of
the `+`−νν final state a correction factor, extracted as a function of mZZ , is used
to reweight the interference distributions obtained at particle-level to account for re-
construction effects. The final expected LWA mT distribution is obtained from the
combination of the interference distributions with simulated mT distributions, which
are interpolated between the simulated mass points with a weighting technique using
the Higgs propagator, a similar method to that used for the interference.
Results Table 8.3 contains the number of observed candidate events along with the
background yields for the `+`−νν analysis, while Figure 8.12 shows the mT distribution
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for the electron and muon channels with the ggF-enriched and VBF-enriched categories
combined.
Table 8.3: `+`−νν search: Number of expected and observed events together with
their statistical and systematic uncertainties, for the ggF- and VBF-enriched cate-
gories.
ProcessggF-enriched categories
VBF-enriched categorye+e− channel µ+µ− channel
ZZ 177 ± 3 ± 21 180 ± 3 ± 21 2.1 ± 0.2 ± 0.7
WZ 93 ± 2 ± 4 99.5 ± 2.3 ± 3.2 1.29 ± 0.04 ± 0.27
WW/tt/Wt/Z → ττ 9.2 ± 2.2 ± 1.4 10.7 ± 2.5 ± 0.9 0.39 ± 0.24 ± 0.26
Z + jets 17 ± 1 ± 11 19 ± 1 ± 17 0.8 ± 0.1 ± 0.5
Other backgrounds 1.12 ± 0.04 ± 0.08 1.03 ± 0.04 ± 0.08 0.03 ± 0.01 ± 0.01
Total background 297 ± 4 ± 24 311 ± 5 ± 27 4.6 ± 0.4 ± 0.9
Observed 320 352 9
8.5.2 Correlation schemes
The combined results are based on a simultaneous fit among different signal
regions defined separately for each analysis. To avoid double-counting, the orthogo-
nality among signal regions is ensured when designing the analysis. The systematic
uncertainties, represented by nuisance parameters, are properly correlated. The ex-
perimental systematic uncertainties due to the same sources are fully correlated be-
tween/within the two analyses. The uncertainties on QCD scale are uncorrelated for
the ggF/VBF signal productions and the ZZ(∗) continuum backgrounds, as the three
processes are evaluated in different QCD scales; but the uncertainties are correlated
for the qq → ZZ(∗) and the gg → ZZ(∗) background. The uncertainties on the par-
ton distribution functions are fully correlated for the ggF signal production and the
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2−10
1−10
1
10
210
310
PreliminaryATLAS1 = 13 TeV, 36.1 fbs
ννe+ e→ ZZ → H
Data
ZZ
WZ
+jetsZ
ττ→Z, tt, Wt, WW
Other backgrounds
Uncertainty
[GeV]ZZ
Tm
400 600 800 1000 1200 1400
Pre
dic
tion
Data
0.5
1
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(a)
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1
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PreliminaryATLAS1 = 13 TeV, 36.1 fbs
νν
µ+
µ → ZZ → H
Data
ZZ
WZ
+jetsZ
ττ→Z, tt, Wt, WW
Other backgrounds
Uncertainty
[GeV]ZZ
Tm
400 600 800 1000 1200 1400
Pre
dic
tion
Data
0.5
1
1.5
(b)
Figure 8.12: Transverse invariant mass distribution in the `+`−νν search for (a) the
electron channel and (b) the muon channel, including events from both the ggF-
enriched and the VBF-enriched categories. The backgrounds are determined following
the description in Section 8.5.1 and the last bin includes the overflow. The error bars
on the data points indicate the statistical uncertainty and markers are drawn at the
bin centre. The systematic uncertainty on the prediction is shown by the hatched
band. The bottom part of the figures shows the ratio of data over expectation.
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gg → ZZ(∗) background as well as for VBF signal production and the qq → ZZ(∗)
background. The uncertainties resulting from data-driven methods are uncorrelated.
A given correlated uncertainty is modeled in the fit by using a nuisance parameter
common to all of the searches.
8.5.3 Impact of the uncertainties on signal cross section
The impact of a systematic uncertainty on the result depends on the production
mode and the mass hypothesis. For the ggF production, at lower masses the luminosity
uncertainty, the modeling uncertainty of the Z boson with associated jets background
and the statistical uncertainty in eµ control region of the `+`−νν final state dominate,
and at higher masses the uncertainties on the electron isolation efficiency become
important, as seen also in the VBF production. For the VBF production, the dominant
uncertainties come from the showering uncertainties and theoretical predictions of the
ZZ events in the VBF category. Additionally at lower masses, the pileup reweighting
and the jet energy resolution uncertainties are also important. Table 8.4 shows the
impact of the leading systematic uncertainties on the signal cross section, which is set
to the expected upper limit, for ggF production and VBF production. The impact of
the uncertainty from the integrated luminosity, 3.2%, enters both in the normalization
of the fitted number of signal events as well as in the background expectation from
simulation. This leads to a luminosity uncertainty which varies from 4% to 7% across
the mass distribution, depending on the signal to background ratio.
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Table 8.4: Impact of the leading systematic uncertainties on the predicted signal
event yield which is set to the expected upper limit, expressed as a percentage of the
cross section for the ggF (left) and VBF (right) production modes at mH = 300, 600,
and 1000 GeV.
ggF production VBF production
Systematic source Impact [%] Systematic source Impact [%]
mH = 300 GeV
Luminosity 4 Parton showering 9
Z+jets modeling (`+`−νν) 3.3 Jet energy scale 4
Parton showering 3.2 Luminosity 4
eµ statistical uncertainty `+`−νν 3.2 qq → ZZ(∗) QCD scale (VBF-enriched category) 4
mH = 600 GeV
Luminosity 6 Parton showering 6
Pileup reweighting 5 Pileup reweighting 6
Z+jets modeling (`+`−νν) 4 Jet energy scale 6
QCD scale of qq → ZZ(∗) 3.1 Luminosity 4
mH = 1000 GeV
Luminosity 4 Parton showering 6
QCD scale of gg → ZZ(∗) 2.3 Jet energy scale 5
Jet vertex tagger 1.9 Z+jets modeling (`+`−νν) 4
Z+jets modeling (`+`−νν) 1.8 Luminosity 4
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8.5.4 Combination results
The excess observed in the `+`−`+`− search at a mass around 700 GeVis excluded
at 95% confidence level by the `+`−νν search, which is more sensitive in this mass
range. The excess at 240 GeV is not covered by the `+`−νν search, the sensitivity
of which starts from 300 GeV. When combining the results from the two final states,
the largest deviation with respect to the background expectation is observed around
700 GeV with a global significance of less than 1 σ and a local significance of about 2 σ.
The combined yield of the two final states is 1870 events observed in data compared to
1643 ± 164 (combined statistical and systematic uncertainty) for the total expected
backgrounds. This corresponds to a 1.3 σ global excess in data. Since no significant
excess is found, the results are interpreted as upper limits on the production cross
section of a scalar resonance. The local p-value for `+`−`+`− and `+`−νν as well as
their combination derived for a narrow resonance and assuming the signal comes only
from the ggF production is shown in Figure 8.13 as a function of the resonance mass
mH between 200 GeV and 1200 GeV.
NWA interpretation Upper limits on the cross section times branching ratio (σ×
BR(H → ZZ )) for a heavy resonance are obtained as a function of mH with the CLs
procedure [149] in the asymptotic approximation from the combination of the two final
states. It is assumed that an additional heavy scalar would be produced predominantly
via the ggF and VBF processes but that the ratio of the two production mechanisms
is unknown in the absence of a specific model. For this reason, fits for the ggF and
VBF production processes are done separately, and in each case the other process is
allowed to float in the fit as an additional nuisance parameter. Figure 8.14 presents
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[GeV]Hm
200 400 600 800 1000 1200
0p
Lo
ca
l
6−10
5−10
4−10
3−10
2−10
1−10
1
σ1
σ2
σ3
σ4
ATLAS1 = 13 TeV, 36.1 fbs
νν
l+
l +
l+
l
l+
l → ZZ → H
NWA
Global significance for
σ): 2.2
l+
l
l+
llargest excess (
l
+l
l
+l
νν
l+
l
Combined
Figure 8.13: Local p0 for `+`−`+`− (blue, dashed line) and `+`−νν (red, dotted
line) final states as well as for their combination (black line) derived for a narrow
resonance and assuming the signal comes only from the ggF production, as a function
of the resonance mass mH between 200 GeV and 1200 GeV. Also shown are local
(dot-dashed line) significance levels.
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[GeV]H
m
200 400 600 800 1000 1200
) [p
b]
ZZ
→
H(B
R
×)
H →
(gg
σ95%
C.L
. lim
it o
n
2−10
1−10
1
10 PreliminaryATLAS
1 = 13 TeV, 36.1 fbs
νν
l+
l +
l+
l
l+
l → ZZ → H
ggF production
limitS
CLObserved
limitS
CLExpected
σ 1±Expected
σ 2±Expected
)
l+
l
l+
l limit (S
CLExpected
)νν
l+
l limit (S
CLExpected
(a)
[GeV]H
m
200 400 600 800 1000 1200
) [p
b]
ZZ
→
H(B
R
×)
H →
(qq
σ95%
C.L
. lim
it o
n
2−10
1−10
1
10 PreliminaryATLAS
1 = 13 TeV, 36.1 fbs
νν
l+
l +
l+
l
l+
l → ZZ → H
VBF production
limitS
CLObserved
limitS
CLExpected
σ 1±Expected
σ 2±Expected
)
l+
l
l+
l limit (S
CLExpected
)νν
l+
l limit (S
CLExpected
(b)
Figure 8.14: The upper limits at 95% confidence level on the cross section times
branching ratio for (a) the ggF production mode (σggF×BR(H → ZZ )) and (b) for
the VBF production mode (σVBF × BR(H → ZZ )) in the case of NWA. The green
and yellow bands represent the ±1σ and ±2σ uncertainties on the expected limits.
The dashed coloured lines indicate the expected limits obtained from the individual
searches.
the expected and observed limits at 95% confidence level on σ ×BR(H → ZZ ) of a
narrow-width scalar for the ggF (left) and VBF (right) production modes, as well as the
expected limits from the `+`−`+`− and `+`−νν searches. This result is valid for models
in which the width is less than 0.5% of mH . When combining both final states, the
95% CL upper limits range from 0.68 pb at mH = 242 GeV to 11 fb at mH = 1200 GeV
for the gluon fusion production mode and from 0.41 pb at mH = 236 GeV to 13 fb
at mH = 1200 GeV for the vector boson fusion production mode. Compared with the
results presented in Run 1 [20] where all four final states of ZZ decays were combined,
the exclusion region presented here is significantly extended, depending on the heavy
scalar mass tested.
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LWA interpretation In the case of the LWA, limits on the cross section for the ggF
production mode times branching ratio (σggF × BR(H → ZZ )) are set for different
widths of the heavy scalar. The interference between the heavy scalar and the SM
Higgs boson, H–h, as well as the heavy scalar and the gg → ZZ(∗) continuum, H–
B, are modelled by either analytical functions or reweighting the signal-only events
as explained in Sections 8.2 and 8.5.1. Figures 8.15(a), 8.15(b), and 8.15(c) show the
limits for a width of 1%, 5% and 10% of mH respectively. The limits are set for masses
of mH higher than 400 GeV.
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[GeV]Hm
400 500 600 700 800 900 1000
) [p
b]Z
Z
→ H(
BR
×)
H →
(gg
σ95
% C
.L. l
imit
on
2−10
1−10
1 PreliminaryATLAS-1 = 13 TeV, 36.1 fbs
νν-l+l + -l+l-l+l → ZZ → H
Hm × = 0.01 HΓLWA,
limitSCLObserved
limitSCLExpected
σ 1±Expected
σ 2±Expected
)-
l+l-
l+l limit (SCLExpected
)νν-l+l limit (SCLExpected
(a)
[GeV]Hm
400 500 600 700 800 900 1000
) [p
b]Z
Z
→ H(
BR
×)
H →
(gg
σ95
% C
.L. l
imit
on
2−10
1−10
1 PreliminaryATLAS-1 = 13 TeV, 36.1 fbs
νν-l+l + -l+l-l+l → ZZ → H
Hm × = 0.05 HΓLWA,
limitSCLObserved
limitSCLExpected
σ 1±Expected
σ 2±Expected
)-
l+l-
l+l limit (SCLExpected
)νν-l+l limit (SCLExpected
(b)
[GeV]Hm
400 500 600 700 800 900 1000
) [p
b]Z
Z
→ H(
BR
×)
H →
(gg
σ95
% C
.L. l
imit
on
2−10
1−10
1 PreliminaryATLAS-1 = 13 TeV, 36.1 fbs
νν-l+l + -l+l-l+l → ZZ → H
Hm × = 0.1 HΓLWA,
limitSCLObserved
limitSCLExpected
σ 1±Expected
σ 2±Expected
)-
l+l-
l+l limit (SCLExpected
)νν-l+l limit (SCLExpected
(c)
Figure 8.15: The 95% confidence level limits on the cross section for the ggF pro-
duction mode times branching ratio (σggF × BR(H → ZZ )) as function of mH for
an additional heavy scalar assuming a width of (a) 1%, (b) 5%, and (c) 10% of mH .
The green and yellow bands represent the ±1σ and ±2σ uncertainties on the ex-
pected limits. The dashed coloured lines indicate the expected limits obtained from
the individual searches.
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Chapter 9
Conclusion
The observation of the SM Higgs boson in the decay channel H→ ZZ(∗) → `+`−`+`−
is presented. It uses pp collision data corresponding to integrated luminosities of
4.5 fb−1and 20.3 fb−1at√s = 7 TeV and
√s = 8 TeV, respectively, recorded with
the ATLAS detector at the LHC. In the mass range 120 — 130 GeV, 37 events are
observed while 26.5 ± 1.7 events are expected, decomposed as 16.2 ± 1.6 events for a
SM Higgs signal with mH = 125 GeV, 7.4 ± 0.4 ZZ(∗) background events and 2.9 ±
0.3 reducible background events. This excess corresponds to a H→ ZZ(∗) → `+`−`+`−
signal observed (expected) with a significance of 8.1 (6.2) standard deviations at the
combined ATLAS measurement of the Higgs boson mass, mH = 125.36 GeV [152].
Furthermore, the mass and different production rates of the observed Higgs boson
is measured. The mass measured in the `+`−`+`− final state using the LHC Run 1
data is mH = 125.51 ± 0.52 GeV. The gluon fusion signal strength is found to be
1.66+0.45−0.41(stat)+0.25
−0.51(syst) and the signal strength for vector-boson fusion is found to
be 0.26+1.60−0.91(stat)+0.36
−0.23(syst). The measured signal strength is consistent with the SM
expected values.
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In the light of the observation of the SM Higgs boson, a search is presented for
additional heavy scalars decaying into a pair of Z bosons which decay subsequently
to `+`−`+`− and `+`−νν final states. The search uses proton–proton collision data
collected with the ATLAS detector during 2015 and 2016 at the Large Hadron Col-
lider at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of
36.1 fb−1. The results of the search are interpreted as upper limits on the production
cross section of a spin-0 resonance. The mass range of the hypothetical resonances con-
sidered is between 200 GeV and 2000 GeV depending on the final state, and the model
considered. The spin-0 resonance is assumed to be a heavy scalar, whose dominant
production modes are gluon fusion and vector boson fusion. In a model independent
approach the spin-0 resonance is studied in the Narrow Width Approximation and the
Large Width Assumption. In the case of the Narrow Width Approximation, limits on
the production rate of a heavy scalar decaying into two Z bosons are set separately for
gluon fusion and vector boson fusion production modes. Combining both final states,
95% CL upper limits range from 0.68 pb at mH = 242 GeV to 11 fb at mH = 1200 GeV
for the gluon fusion production mode and from 0.41 pb at mH = 236 GeV to 13 fb
at mH = 1200 GeV for the vector boson fusion production mode. The results are
also interpreted in the context of Type-I and Type-II two-Higgs-doublet models, with
exclusion contours given in the cos(β − α) versus tan β (for mH = 200 GeV) and mH
versus tan β planes. This mH value is chosen so that the assumption of a narrow-width
Higgs boson is valid over most of the parameter space and the experimental sensitivity
is maximum. The limits on the production rate of a large-width scalar are obtained
for widths of 1%, 5% and 10% of the mass of the resonance, with the interference
between the heavy scalar and the SM Higgs boson as well as the heavy scalar and the
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gg → ZZ(∗) continuum taken into account.
Page 150
124
Bibliography
[1] F. Englert and R. Brout, Broken Symmetry and the Mass of Gauge Vector
Mesons , Phys. Rev. Lett. 13 (1964) 321–323.
[2] P. W. Higgs, Broken symmetries, massless particles and gauge fields , Phys.
Lett. 12 (1964) 132–133.
[3] P. W. Higgs, Broken Symmetries and the Masses of Gauge Bosons , Phys. Rev.
Lett. 13 (1964) 508–509.
[4] G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Global Conservation Laws
and Massless Particles , Phys. Rev. Lett. 13 (1964) 585–587.
[5] P. W. Higgs, Spontaneous Symmetry Breakdown without Massless Bosons ,
Phys. Rev. 145 (1966) 1156–1163.
[6] S. L. Glashow, Partial Symmetries of Weak Interactions , Nucl. Phys. 22
(1961) 579–588.
[7] S. Weinberg, A Model of Leptons , Phys. Rev. Lett. 19 (1967) 1264–1266.
[8] A. Salam, Weak and Electromagnetic Interactions , Conf. Proc. C680519
(1968) 367–377.
Page 151
125
[9] L. Evans and P. Bryant, LHC Machine, JINST 3 (2008) S08001.
[10] ALEPH and CDF and D0 and DELPHI and L3 and OPAL and SLD
Collaborations and LEP Electroweak Working Group and Tevatron
Electroweak Working Group and SLD Electroweak and Heavy Flavour Groups
Collaboration, L. E. W. Group, Precision Electroweak Measurements and
Constraints on the Standard Model , arXiv:1012.2367 [hep-ex].
[11] ALEPH and DELPHI and L3 and OPAL Collaborations and LEP Working
Group for Higgs boson searches Collaboration, R. Barate et al., Search for the
standard model Higgs boson at LEP , Phys. Lett. B565 (2003) 61–75,
arXiv:hep-ex/0306033 [hep-ex].
[12] ATLAS Collaboration, Observation of a new particle in the search for the
Standard Model Higgs boson with the ATLAS detector at the LHC , Phys. Lett.
B 716 (2012) 1, arXiv:1207.7214 [hep-ex].
[13] CMS Collaboration, Observation of a new boson at a mass of 125 GeV with
the CMS experiment at the LHC , Phys. Lett. B 716 (2012) 30,
arXiv:1207.7235 [hep-ex].
[14] ATLAS and CMS Collaborations, Combined Measurement of the Higgs Boson
Mass in pp Collisions at√s = 7 and 8 TeV with the ATLAS and CMS
Experiments , Phys. Rev. Lett. 114 (2015) 191803, arXiv:1503.07589
[hep-ex].
Page 152
126
[15] ATLAS Collaboration, Study of the spin and parity of the Higgs boson in
diboson decays with the ATLAS detector , Eur. Phys. J. C 75 (2015) 476,
arXiv:1506.05669 [hep-ex].
[16] CMS Collaboration, Study of the Mass and Spin-Parity of the Higgs Boson
Candidate Via Its Decays to Z Boson Pairs , Phys. Rev. Lett. 110 (2013)
081803, arXiv:1212.6639 [hep-ex].
[17] CMS Collaboration, Observation of the diphoton decay of the Higgs boson and
measurement of its properties , Eur. Phys. J. C 74 (2014) 3076,
arXiv:1407.0558 [hep-ex].
[18] ATLAS Collaboration, Test of CP invariance in vector-boson fusion production
of the Higgs boson using the Optimal Observable method in the ditau decay
channel with the ATLAS detector , The European Physical Journal C 76 (2016)
no. 12, 658.
[19] ATLAS and CMS Collaborations, Measurements of the Higgs boson production
and decay rates and constraints on its couplings from a combined ATLAS and
CMS analysis of the LHC pp collision data at√s = 7 and 8 TeV, JHEP 08
(2016) 045, arXiv:1606.02266 [hep-ex].
[20] ATLAS Collaboration, Search for an additional, heavy Higgs boson in the
H → ZZ decay channel at√s = 8 TeV in pp collision data with the ATLAS
detector , Eur. Phys. J. C 76 (2016) 45, arXiv:1507.05930 [hep-ex].
Page 153
127
[21] CMS Collaboration, Search for a Higgs boson in the mass range from 145 to
1000 GeV decaying to a pair of W or Z bosons , JHEP 10 (2015) 144,
arXiv:1504.00936 [hep-ex].
[22] G. ’t Hooft and M. J. G. Veltman, Regularization and Renormalization of
Gauge Fields , Nucl. Phys. B44 (1972) 189–213.
[23] C.-N. Yang and R. L. Mills, Conservation of Isotopic Spin and Isotopic Gauge
Invariance, Phys. Rev. 96 (1954) 191–195.
[24] M. Gell-Mann, A Schematic Model of Baryons and Mesons , Phys. Lett. 8
(1964) 214–215.
[25] G. Zweig, An SU(3) model for strong interaction symmetry and its breaking , in
CERN-TH-401, CERN-TH-412. 1964.
[26] T. W. B. Kibble, Symmetry breaking in nonAbelian gauge theories , Phys. Rev.
155 (1967) 1554.
[27] UA1 Collaboration, Experimental Observation of Isolated Large Transverse
Energy Electrons with Associated Missing Energy at√s = 540 GeV , Phys.
Lett. 122B (1983) 103–116.
[28] UA2 Collaboration, Observation of Single Isolated Electrons of High
Transverse Momentum in Events with Missing Transverse Energy at the
CERN pp Collider , Phys. Lett. 122B (1983) 476–485.
Page 154
128
[29] UA1 Collaboration, Experimental Observation of Lepton Pairs of Invariant
Mass Around 95 GeV/c2 at the CERN SPS Collider , Phys. Lett. 126B (1983)
398–410.
[30] UA2 Collaboration, Evidence for Z0 → e+e− at the CERN pp Collider , Phys.
Lett. 129B (1983) 130–140.
[31] LHC Higgs Cross Section Working Group, S. Dittmaier, C. Mariotti,
G. Passarino, and R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections: 1.
Inclusive Observables , CERN-2011-002 (2011) , arXiv:1101.0593 [hep-ph].
[32] LHC Higgs Cross Section Working Group, S. Dittmaier, C. Mariotti,
G. Passarino, and R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections:
2. Differential Distributions , CERN-2012-002 (2012) , arXiv:1201.3084
[hep-ph].
[33] LHC Higgs Cross Section Working Group, S. Heinemeyer, C. Mariotti,
G. Passarino, and R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections:
3. Higgs Properties , CERN-2013-004 (CERN, Geneva, 2013) ,
arXiv:1307.1347 [hep-ph].
[34] LHC Higgs Cross Section Working Group, S. Heinemeyer, C. Mariotti,
G. Passarino, and R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections:
4. Deciphering the Nature of the Higgs Sector , arXiv:1610.07922 [hep-ph].
[35] H. M. Georgi, S. L. Glashow, M. E. Machacek, and D. V. Nanopoulos, Higgs
Bosons from Two Gluon Annihilation in Proton Proton Collisions , Phys. Rev.
Lett. 40 (1978) 692.
Page 155
129
[36] A. Djouadi, M. Spira, and P. M. Zerwas, Production of Higgs bosons in proton
colliders: QCD corrections , Phys. Lett. B264 (1991) 440–446.
[37] S. Dawson, Radiative corrections to Higgs boson production, Nucl. Phys. B359
(1991) 283–300.
[38] M. Spira, A. Djouadi, D. Graudenz, and P. M. Zerwas, Higgs boson production
at the LHC , Nucl. Phys. B453 (1995) 17–82, arXiv:hep-ph/9504378.
[39] R. V. Harlander and W. B. Kilgore, Next-to-next-to-leading order Higgs
production at hadron colliders , Phys. Rev. Lett. 88 (2002) 201801,
arXiv:hep-ph/0201206.
[40] C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in
NNLO QCD , Nucl. Phys. B646 (2002) 220–256, arXiv:hep-ph/0207004.
[41] V. Ravindran, J. Smith, and W. L. van Neerven, NNLO corrections to the total
cross-section for Higgs boson production in hadron hadron collisions , Nucl.
Phys. B665 (2003) 325–366, arXiv:hep-ph/0302135.
[42] U. Aglietti, R. Bonciani, G. Degrassi, and A. Vicini, Two loop light fermion
contribution to Higgs production and decays , Phys. Lett. B595 (2004) 432–441,
arXiv:hep-ph/0404071.
[43] S. Actis, G. Passarino, C. Sturm, and S. Uccirati, NLO Electroweak
Corrections to Higgs Boson Production at Hadron Colliders , Phys. Lett. B670
(2008) 12–17, arXiv:0809.1301 [hep-ph].
Page 156
130
[44] S. Catani, D. de Florian, M. Grazzini, and P. Nason, Soft gluon resummation
for Higgs boson production at hadron colliders , JHEP 07 (2003) 028,
arXiv:hep-ph/0306211.
[45] C. Anastasiou, R. Boughezal, and F. Petriello, Mixed QCD-electroweak
corrections to Higgs boson production in gluon fusion, JHEP 04 (2009) 003,
arXiv:0811.3458 [hep-ph].
[46] D. de Florian and M. Grazzini, Higgs production at the LHC: updated cross
sections at√s = 8 TeV , Phys. Lett. B718 (2012) 117–120, arXiv:1206.4133
[hep-ph].
[47] C. Anastasiou, S. Buehler, F. Herzog, and A. Lazopoulos, Inclusive Higgs
boson cross-section for the LHC at 8 TeV , JHEP 04 (2012) 004,
arXiv:1202.3638 [hep-ph].
[48] J. Baglio and A. Djouadi, Higgs production at the lHC , JHEP 03 (2011) 055,
arXiv:1012.0530 [hep-ph].
[49] D. de Florian, G. Ferrera, M. Grazzini, and D. Tommasini,
Transverse-momentum resummation: Higgs boson production at the Tevatron
and the LHC , JHEP 11 (2011) 064, arXiv:1109.2109 [hep-ph].
[50] E. Bagnaschi, G. Degrassi, P. Slavich, and A. Vicini, Higgs production via
gluon fusion in the POWHEG approach in the SM and in the MSSM , JHEP
02 (2012) 088, arXiv:1111.2854 [hep-ph].
Page 157
131
[51] R. N. Cahn and S. Dawson, Production of Very Massive Higgs Bosons , Phys.
Lett. 136B (1984) 196. [Erratum: Phys. Lett.138B,464(1984)].
[52] M. Ciccolini, A. Denner, and S. Dittmaier, Strong and electroweak corrections
to the production of Higgs + 2jets via weak interactions at the LHC , Phys.
Rev. Lett. 99 (2007) 161803, arXiv:0707.0381 [hep-ph].
[53] M. Ciccolini, A. Denner, and S. Dittmaier, Electroweak and QCD corrections
to Higgs production via vector-boson fusion at the LHC , Phys. Rev. D77
(2008) 013002, arXiv:0710.4749 [hep-ph].
[54] K. Arnold et al., VBFNLO: A Parton level Monte Carlo for processes with
electroweak bosons , Comput. Phys. Commun. 180 (2009) 1661–1670,
arXiv:0811.4559 [hep-ph].
[55] P. Bolzoni, F. Maltoni, S.-O. Moch, and M. Zaro, Higgs production via
vector-boson fusion at NNLO in QCD , Phys. Rev. Lett. 105 (2010) 011801,
arXiv:1003.4451 [hep-ph].
[56] S. L. Glashow, D. V. Nanopoulos, and A. Yildiz, Associated Production of
Higgs Bosons and Z Particles , Phys. Rev. D18 (1978) 1724–1727.
[57] T. Han and S. Willenbrock, QCD correction to the p p —¿ W H and Z H total
cross-sections , Phys. Lett. B273 (1991) 167–172.
[58] O. Brein, A. Djouadi, and R. Harlander, NNLO QCD corrections to the
Higgs-strahlung processes at hadron colliders , Phys. Lett. B579 (2004)
149–156, arXiv:hep-ph/0307206.
Page 158
132
[59] M. L. Ciccolini, S. Dittmaier, and M. Kramer, Electroweak radiative
corrections to associated WH and ZH production at hadron colliders , Phys.
Rev. D68 (2003) 073003, arXiv:hep-ph/0306234.
[60] Z. Kunszt, Associated Production of Heavy Higgs Boson with Top Quarks ,
Nucl. Phys. B247 (1984) 339–359.
[61] W. Beenakker, S. Dittmaier, M. Kramer, B. Plumper, M. Spira, and P. M.
Zerwas, Higgs radiation off top quarks at the Tevatron and the LHC , Phys.
Rev. Lett. 87 (2001) 201805, arXiv:hep-ph/0107081.
[62] W. Beenakker, S. Dittmaier, M. Kramer, B. Plumper, M. Spira, and P. M.
Zerwas, NLO QCD corrections to t anti-t H production in hadron collisions ,
Nucl. Phys. B653 (2003) 151–203, arXiv:hep-ph/0211352.
[63] S. Dawson, L. H. Orr, L. Reina, and D. Wackeroth, Associated top quark Higgs
boson production at the LHC , Phys. Rev. D67 (2003) 071503,
arXiv:hep-ph/0211438.
[64] S. Dawson, C. Jackson, L. H. Orr, L. Reina, and D. Wackeroth, Associated
Higgs production with top quarks at the large hadron collider: NLO QCD
corrections , Phys. Rev. D68 (2003) 034022, arXiv:hep-ph/0305087.
[65] ATLAS Collaboration, G. Aad et al., Search for the Standard Model Higgs
boson decaying into bb produced in association with top quarks decaying
hadronically in pp collisions at√s = 8 TeV with the ATLAS detector , JHEP
05 (2016) 160, arXiv:1604.03812 [hep-ex].
Page 159
133
[66] CMS Collaboration, Search for the associated production of the Higgs boson
with a top-quark pair , JHEP 09 (2014) 087, arXiv:1408.1682 [hep-ex].
[Erratum: JHEP10,106(2014)].
[67] Branco et al., Theory and phenomenology of two-Higgs-doublet models , Phys.
Rept. 516 (2012) 1–102, arXiv:1106.0034 [hep-ph].
[68] H. E. Haber and G. L. Kane, The Search for Supersymmetry: Probing Physics
Beyond the Standard Model , Phys. Rept. 117 (1985) 75–263.
[69] R. V. Harlander, S. Liebler, and H. Mantler, SusHi: A program for the
calculation of Higgs production in gluon fusion and bottom-quark annihilation
in the Standard Model and the MSSM , Comput. Phys. Commun. 184 (2013)
1605–1617, arXiv:1212.3249 [hep-ph].
[70] R. V. Harlander and W. B. Kilgore, Higgs boson production in bottom quark
fusion at next-to-next-to leading order , Phys. Rev. D68 (2003) 013001,
arXiv:hep-ph/0304035.
[71] R. Bonciani, G. Degrassi, and A. Vicini, On the Generalized Harmonic
Polylogarithms of One Complex Variable, Comput. Phys. Commun. 182 (2011)
1253–1264, arXiv:1007.1891.
[72] R. Harlander and P. Kant, Higgs production and decay: Analytic results at
next-to-leading order QCD , JHEP 12 (2005) 015, arXiv:hep-ph/0509189.
Page 160
134
[73] D. Eriksson, J. Rathsman, and O. Stal, 2HDMC: Two-Higgs-Doublet Model
Calculator Physics and Manual , Comput. Phys. Commun. 181 (2010)
189–205, arXiv:0902.0851 [hep-ph].
[74] J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization of Hard Processes
in QCD , Adv. Ser. Direct. High Energy Phys. 5 (1989) 1–91,
arXiv:hep-ph/0409313 [hep-ph].
[75] V. N. Gribov and L. N. Lipatov, Deep inelastic ep scattering in perturbation
theory , Sov. J. Nucl. Phys. 15 (1972) 438–450. [Yad. Fiz.15,781(1972)].
[76] D. J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge
Theories , Phys. Rev. Lett. 30 (1973) 1343–1346.
[77] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, MadGraph 5 :
Going Beyond , JHEP 06 (2011) 128, arXiv:1106.0522 [hep-ph].
[78] S. van der Meer, Calibration of the Effective Beam Height in the ISR, .
[79] C. Rubbia, Measurement of the Luminosity of p anti-p Collider with a
(Generalized) Van Der Meer Method , .
[80] ATLAS Collaboration, Luminosity determination in pp collisions at
√s = 7 TeV using the ATLAS detector at the LHC , Eur. Phys. J. C 71 (2011)
1630, arXiv:1101.2185 [hep-ex].
[81] ATLAS Collaboration, Improved luminosity determination in pp collisions at
√s = 7 TeV using the ATLAS detector at the LHC , Eur. Phys. J. C 73 (2013)
2518, arXiv:1302.4393 [hep-ex].
Page 161
135
[82] ATLAS Collaboration, Luminosity determination in pp collisions at
√s = 8 TeV using the ATLAS detector at the LHC , Eur. Phys. J. C 76 (2016)
653, arXiv:1608.03953 [hep-ex].
[83] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron
Collider , JINST 3 (2008) S08003.
[84] M. Capeans, G. Darbo, K. Einsweiller, M. Elsing, T. Flick, M. Garcia-Sciveres,
C. Gemme, H. Pernegger, O. Rohne, and R. Vuillermet, ATLAS Insertable
B-Layer Technical Design Report , Tech. Rep. CERN-LHCC-2010-013.
ATLAS-TDR-19, Sep, 2010. https://cds.cern.ch/record/1291633.
[85] ATLAS Collaboration, Track Reconstruction Performance of the ATLAS Inner
Detector at√s = 13 TeV , Tech. Rep. ATL-PHYS-PUB-2015-018, Geneva, Jul,
2015.
[86] ATLAS Collaboration, G. Aad et al., Improved luminosity determination in pp
collisions at sqrt(s) = 7 TeV using the ATLAS detector at the LHC , Eur.
Phys. J. C73 (2013) no. 8, 2518, arXiv:1302.4393 [hep-ex].
[87] ATLAS Collaboration, The ATLAS Simulation Infrastructure, Eur. Phys. J.
C70 (2010) 823–874, arXiv:1005.4568 [physics.ins-det].
[88] J. Alwall et al., A Standard format for Les Houches event files , Comput. Phys.
Commun. 176 (2007) 300–304, arXiv:hep-ph/0609017.
[89] S. Agostinelli et al., GEANT4: A simulation toolkit , Nucl. Instrum. Meth.
A 506 (2003) 250–303.
Page 162
136
[90] J. Allison et al., Geant4 developments and applications , IEEE Trans. Nucl. Sci.
53 (2006) 270.
[91] T. Sjostrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten,
S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, An Introduction to
PYTHIA 8.2 , Comput. Phys. Commun. 191 (2015) 159–177,
arXiv:1410.3012 [hep-ph].
[92] ATLAS Collaboration, ATLAS Pythia8 tunes to 7 TeV data,
ATL-PHYS-PUB-2014-021, 2014. https://cds.cern.ch/record/1966419.
[93] R. D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B 867
(2013) 244, arXiv:1207.1303 [hep-ph].
[94] ATLAS Collaboration, Measurement of the Z/γ∗ boson transverse momentum
distribution in pp collisions at√s = 7 TeV with the ATLAS detector , JHEP
09 (2014) 145, arXiv:1406.3660 [hep-ex].
[95] J. Pumplin et al., New generation of parton distributions with uncertainties
from global QCD analysis , JHEP 07 (2002) 012, arXiv:hep-ph/0201195.
[96] P. Nason, A New method for combining NLO QCD with shower Monte Carlo
algorithms , JHEP 11 (2004) 040, arXiv:hep-ph/0409146.
[97] S. Frixione, P. Nason, and C. Oleari, Matching NLO QCD computations with
Parton Shower simulations: the POWHEG method , JHEP 11 (2007) 070,
arXiv:0709.2092 [hep-ph].
Page 163
137
[98] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum.
Meth. A462 (2001) 152–155.
[99] S. Alioli, P. Nason, C. Oleari, and E. Re, NLO Higgs boson production via
gluon fusion matched with shower in POWHEG , JHEP 04 (2009) 002,
arXiv:0812.0578 [hep-ph].
[100] P. Nason and C. Oleari, NLO Higgs boson production via vector-boson fusion
matched with shower in POWHEG , JHEP 02 (2010) 037, arXiv:0911.5299
[hep-ph].
[101] D. de Florian, G. Ferrera, M. Grazzini, and D. Tommasini, Higgs boson
production at the LHC: transverse momentum resummation effects in the
H-¿2gamma, H-¿WW-¿lnu lnu and H-¿ZZ-¿4l decay modes , JHEP 06 (2012)
132, arXiv:1203.6321 [hep-ph].
[102] M. Grazzini and H. Sargsyan, Heavy-quark mass effects in Higgs boson
production at the LHC , JHEP 09 (2013) 129, arXiv:1306.4581 [hep-ph].
[103] T. Sjostrand, S. Mrenna, and P. Z. Skands, A Brief Introduction to PYTHIA
8.1 , Comput. Phys. Commun. 178 (2008) 852–867, arXiv:0710.3820
[hep-ph].
[104] P. Golonka and Z. Was, PHOTOS Monte Carlo: A Precision tool for QED
corrections in Z and W decays , Eur. Phys. J. C45 (2006) 97–107,
arXiv:hep-ph/0506026.
Page 164
138
[105] N. Davidson, T. Przedzinski, and Z. Was, PHOTOS interface in C++:
Technical and Physics Documentation, Comput. Phys. Commun. 199 (2016)
86–101, arXiv:1011.0937 [hep-ph].
[106] J. A. et al, The automated computation of tree-level and next-to-leading order
differential cross sections, and their matching to parton shower simulations ,
arXiv:1405.0301 [hep-ph].
[107] R. Frederix and S. Frixione, Merging meets matching in MC@NLO , JHEP 12
(2012) 061, arXiv:1209.6215 [hep-ph].
[108] T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann, F. Siegert,
and J. Winter, Event generation with SHERPA 1.1 , JHEP 02 (2009) 007,
arXiv:0811.4622 [hep-ph].
[109] T. Gleisberg and S. Hoche, Comix, a new matrix element generator , JHEP
0812 (2008) 039, arXiv:0808.3674 [hep-ph].
[110] F. Cascioli, P. Maierhofer, and S. Pozzorini, Scattering Amplitudes with Open
Loops , Phys. Rev. Lett. 108 (2012) 111601, arXiv:1111.5206 [hep-ph].
[111] NNPDF Collaboration, R. D. Ball et al., Parton distributions for the LHC Run
II , JHEP 04 (2015) 040, arXiv:1410.8849 [hep-ph].
[112] S. Schumann and F. Krauss, A Parton shower algorithm based on
Catani-Seymour dipole factorisation, JHEP 0803 (2008) 038,
arXiv:0709.1027 [hep-ph].
Page 165
139
[113] S. Hoche, F. Krauss, M. Schonherr, and F. Siegert, QCD matrix elements +
parton showers: The NLO case, JHEP 04 (2013) 027, arXiv:1207.5030
[hep-ph].
[114] B. Biedermann, A. Denner, S. Dittmaier, L. Hofer, and B. Jager, Electroweak
corrections to pp→ µ+µ−e+e− +X at the LHC: a Higgs background study ,
Phys. Rev. Lett. 116 (2016) 161803, arXiv:1601.07787 [hep-ph].
[115] B. Biedermann, A. Denner, S. Dittmaier, L. Hofer, and B. Jager,
Next-to-leading-order electroweak corrections to the production of four charged
leptons at the LHC , JHEP 01 (2017) 033, arXiv:1611.05338 [hep-ph].
[116] F. Caola, K. Melnikov, R. Rontsch, and L. Tancredi, QCD corrections to ZZ
production in gluon fusion at the LHC , Phys. Rev. D92 (2015) 094028,
arXiv:1509.06734 [hep-ph].
[117] J. M. Campbell, R. K. Ellis, M. Czakon, and S. Kirchner, Two Loop Correction
to Interference in gg → ZZ, arXiv:1605.01380 [hep-ph].
[118] S. Alioli et al., ZZ production in gluon fusion at NLO matched to
parton-shower , Phys. Rev. D95 (2017) no. 3, 034042, arXiv:1609.09719
[hep-ph].
[119] K. Melnikov and M. Dowling, Production of two Z-bosons in gluon fusion in
the heavy top quark approximation, Phys. Lett. B744 (2015) 43–47,
arXiv:1503.01274 [hep-ph].
Page 166
140
[120] C. S. Li, H. T. Li, D. Y. Shao, and J. Wang, Soft gluon resummation in the
signal-background interference process of gg(→ h∗)→ ZZ , JHEP 08 (2015) 065,
arXiv:1504.02388 [hep-ph].
[121] T. Sjostrand, S. Mrenna, and P. Z. Skands, PYTHIA 6.4 Physics and Manual ,
JHEP 05 (2006) 026, arXiv:hep-ph/0603175.
[122] ATLAS Collaboration, Electron efficiency measurements with the ATLAS
detector using the 2012 LHC proton-proton collision data, tech. rep., 2017.
arXiv:1612.01456 [hep-ex].
[123] ATLAS Collaboration, Electron efficiency measurements with the ATLAS
detector using the 2015 LHC proton–proton collision data,
ATLAS-CONF-2016-024, 2016. https://cds.cern.ch/record/2157687.
[124] ATLAS Collaboration, Measurement of the muon reconstruction performance
of the ATLAS detector using 2011 and 2012 LHC proton–proton collision data,
Eur. Phys. J. C 74 (2014) 3130, arXiv:1407.3935 [hep-ex].
[125] ATLAS Collaboration, Muon reconstruction performance of the ATLAS
detector in proton–proton collision data at√s = 13 TeV, Eur. Phys. J. C 76
(2016) 292, arXiv:1603.05598 [hep-ex].
[126] M. Cacciari, G. P. Salam, and G. Soyez, The Anti-k(t) jet clustering algorithm,
JHEP 04 (2008) 063, arXiv:0802.1189 [hep-ph].
[127] M. Cacciari, G. P. Salam, and G. Soyez, FastJet User Manual , Eur. Phys. J.
C72 (2012) 1896, arXiv:1111.6097 [hep-ph].
Page 167
141
[128] ATLAS Collaboration, Topological cell clustering in the ATLAS calorimeters
and its performance in LHC Run 1 , Eur. Phys. J. C77 (2017) 490,
arXiv:1603.02934 [hep-ex].
[129] ATLAS Collaboration, Jet energy measurement with the ATLAS detector in
proton-proton collisions at√s = 7 TeV , Eur. Phys. J. C73 (2013) no. 3, 2304,
arXiv:1112.6426 [hep-ex].
[130] ATLAS Collaboration, Jet energy scale measurements and their systematic
uncertainties in proton-proton collisions at√s = 13 TeV with the ATLAS
detector , arXiv:1703.09665 [hep-ex].
[131] ATLAS Collaboration, Jet energy measurement and its systematic uncertainty
in proton-proton collisions at√s = 7 TeV with the ATLAS detector , Eur.
Phys. J. C75 (2015) 17, arXiv:1406.0076 [hep-ex].
[132] ATLAS Collaboration, Characterisation and mitigation of beam-induced
backgrounds observed in the ATLAS detector during the 2011 proton-proton
run, JINST 8 (2013) P07004, arXiv:1303.0223 [hep-ex].
[133] ATLAS Collaboration, Selection of jets produced in 13 TeV proton-proton
collisions with the ATLAS detector , ATLAS-CONF-2015-029, 2015.
https://cds.cern.ch/record/2037702.
[134] ATLAS Collaboration, Tagging and suppression of pileup jets with the ATLAS
detector , ATLAS-CONF-2014-018, 2014.
http://cdsweb.cern.ch/record/1700870.
Page 168
142
[135] M. Cacciari and G. P. Salam, Pileup subtraction using jet areas , Phys. Lett.
B 659 (2008) 119, arXiv:0707.1378 [hep-ph].
[136] ATLAS Collaboration, Reconstruction of collinear final-state-radiation photons
in Z decays to muons in sqrts=7 TeV proton-proton collisions.,
ATLAS-CONF-2012-143, 2012. https://cds.cern.ch/record/1491697.
[137] F. Cascioli, T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhofer, A. von
Manteuffel, S. Pozzorini, D. Rathlev, L. Tancredi, and E. Weihs, ZZ
production at hadron colliders in NNLO QCD , Phys. Lett. B735 (2014)
311–313, arXiv:1405.2219 [hep-ph].
[138] M. Grazzini, S. Kallweit, and D. Rathlev, ZZ production at the LHC: fiducial
cross sections and distributions in NNLO QCD , Phys. Lett. B750 (2015)
407–410, arXiv:1507.06257 [hep-ph].
[139] M. Pivk and F. R. Le Diberder, SPlot: A Statistical tool to unfold data
distributions , Nucl. Instrum. Meth. A555 (2005) 356–369,
arXiv:physics/0402083 [physics.data-an].
[140] E. Gross and O. Vitells, Trial factors or the look elsewhere effect in high energy
physics , Eur. Phys. J. C70 (2010) 525–530, arXiv:1005.1891
[physics.data-an].
[141] ATLAS Collaboration, Procedure for the LHC Higgs boson search combination
in summer 2011 , tech. rep., 2011.
Page 169
143
[142] ATLAS Collaboration, Combined search for the Standard Model Higgs boson in
pp collisions at√s = 7 TeV with the ATLAS detector , Phys. Rev. D 86 (2012)
032003, arXiv:1207.0319 [hep-ex].
[143] D. K. W. Verkerke, The RooFit toolkit for data modeling , tech. rep., 2003.
arXiv:physics/0306116 [physics.data-an].
[144] L. Moneta, K. Belasco, K. S. Cranmer, S. Kreiss, A. Lazzaro, D. Piparo,
G. Schott, W. Verkerke, and M. Wolf, The RooStats Project , tech. rep., 2010.
arXiv:1009.1003 [physics.data-an].
[145] J. Neyman and E. S. Pearson, On the Problem of the Most Efficient Tests of
Statistical Hypotheses , Philosophical Transactions of the Royal Society of
London. Series A, Containing Papers of a Mathematical or Physical Character
231 (1933) 289–337.
[146] S. S. Wilks, The Large-Sample Distribution of the Likelihood Ratio for Testing
Composite Hypotheses , Annals Math. Statist. 9 (1938) no. 1, 60–62.
[147] A. Wald, Tests of Statistical Hypotheses Concerning Several Parameters When
the Number of Observations is Large, Transactions of the American
Mathematical Society 54 (1943) no. 3, 426–482.
[148] Cowan, Glen and Cranmer, Kyle and Gross, Eilam and Vitells, Ofer,
Asymptotic formulae for likelihood-based tests of new physics , Eur. Phys. J.
C71 (2011) 1554, arXiv:1007.1727 [physics.data-an].
Page 170
144
[149] A. L. Read, Presentation of search results: The CL(s) technique, J. Phys. G28
(2002) 2693–2704. [,11(2002)].
[150] ATLAS Collaboration, Search for the Standard Model Higgs boson in the decay
channel H → ZZ(∗) → 4` with the ATLAS detector , Phys. Lett. B 705 (2011)
435, arXiv:1109.5945 [hep-ex].
[151] ATLAS Collaboration, Search for the Standard Model Higgs boson in the decay
channel H → ZZ(∗) → 4` with 4.8 fb−1 of pp collision data at√s = 7 TeV with
ATLAS , Phys. Lett. B 710 (2012) 383, arXiv:1202.1415 [hep-ex].
[152] ATLAS Collaboration, Measurement of the Higgs boson mass from the
H → γγ and H → ZZ∗ → 4` channels in pp collisions at center-of-mass
energies of 7 and 8 TeV with the ATLAS detector , Phys. Rev. D 90 (2014)
052004, arXiv:1406.3827 [hep-ex].
[153] P. Speckmayer, A. Hocker, J. Stelzer, and H. Voss, The toolkit for multivariate
data analysis, TMVA 4 , J. Phys. Conf. Ser. 219 (2010) 032057.
[154] ATLAS Collaboration, Evidence for the spin-0 nature of the Higgs boson using
ATLAS data, Phys. Lett. B 726 (2013) 120, arXiv:1307.1432 [hep-ex].
[155] K. S. Cranmer, Kernel estimation in high-energy physics , Comput. Phys.
Commun. 136 (2001) 198–207, arXiv:hep-ex/0011057 [hep-ex].
[156] A. Hill and J. Van Der Bij, Strongly interacting singlet doublet Higgs model ,
Phys. Rev. D 36 (1987) 3463–3473.
Page 171
145
[157] M. Oreglia, A Study of the Reactions ψ′ → γγψ, 1980.
https://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-236.pdf.
[158] J. Gaiser, Charmonium Spectroscopy From Radiative Decays of the J/ψ and
ψ′, 1982.
https://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-255.pdf.
[159] S. Goria, G. Passarino, and D. Rosco, The Higgs Boson Lineshape, Nucl.Phys.
B864 (2012) 530–579, arXiv:1112.5517 [hep-ph].
[160] N. Kauer and C. OBrien, Heavy Higgs signal-background interference in
gg → V V in the Standard Model plus real singlet , Eur. Phys. J. C 75 (2015)
374, arXiv:1502.04113 [hep-ph].
[161] ATLAS Collaboration, Muon reconstruction performance of the ATLAS
detector in protonproton collision data at√s =13 TeV , Eur. Phys. J. C76
(2016) no. 5, 292, arXiv:1603.05598 [hep-ex].
[162] A. Collaboration, Electron efficiency measurements with the ATLAS detector
using 2012 LHC proton-proton collision data, arXiv:1612.01456 [hep-ex].
[163] M. Bahr et al., Herwig++ physics and manual , Eur. Phys. J. C58 (2008)
639–707, arXiv:0803.0883 [hep-ph].
[164] ATLAS and CMS Collaboration, Measurements of the Higgs boson production
and decay rates and constraints on its couplings from a combined ATLAS and
CMS analysis of the LHC pp collision data at√s = 7 and 8 TeV, JHEP 08
(2016) 045, arXiv:1606.02266 [hep-ex].
Page 172
146
[165] ATLAS Collaboration, M. Aaboud et al., Search for an invisibly decaying
Higgs boson or dark matter candidates produced in association with a Z boson
in pp collisions at√s = 13 TeV with the ATLAS detector , Phys. Lett. B776
(2018) 318–337, arXiv:1708.09624 [hep-ex].
[166] ATLAS Collaboration, Measurements of Wγ and Zγ production in pp
collisions at√s = 7 TeV with the ATLAS detector at the LHC , Phys. Rev. D
87 (2013) 112003, arXiv:1302.1283 [hep-ex].
[167] ATLAS Collaboration, Measurement of the W+W− Cross Section in
√s = 7 TeV pp Collisions with ATLAS , Phys. Rev. Lett. 107 (2011) 041802,
arXiv:1104.5225 [hep-ex].
[168] M. Baak, S. Gadatsch, R. Harrington, and W. Verkerke, Interpolation between
multi-dimensional histograms using a new non-linear moment morphing
method , Nucl. Instrum. Meth. A771 (2015) 39–48, arXiv:1410.7388
[physics.data-an].
